Wire fault detection

ABSTRACT

Described are techniques used in a wire diagnostics system to detect events, such as defects, that may occur within a wire or cable under test. An incident voltage signal is sent out on the wire and a measured voltage signal is obtained which includes the incident voltage and the reflected voltage. Compensation processing is performed on the measured waveform to remove unwanted reflective components. Additionally, the waveform is then subject to attenuation processing and event detection processing. Detected events, such as defects, are classified and output as results. Events are classified by parametric classification using a library of known events or faults. The library of known events or faults is previously generated using empirical analysis and modeling techniques. Additionally, joint time-frequency domain reflectometry (TFDR) techniques are described for event identification and classification for a wire under test.

BACKGROUND OF THE INVENTION

1. Technical Field

This application relates to the field of diagnostics, and moreparticularly to the field of diagnostics that determine the condition ofcables and wires.

2. Description of Related Art

Wiring systems may be used in a variety of industries, such as theaviation and aircraft industry. Different devices and components may becontrolled, monitored and/or enabled using the wiring systems. Existingwiring systems may experience problems that are difficult to detect anddiagnose.

One existing technique is detection of problems through visualinspections, for example, as in connection with general procedures andinspections of aircraft wiring systems. However, defects may goundetected and may only be detected after a system failure or after amore noticeable amount of damage has occurred.

It may be desirable for a variety of different reasons, including safetyconsiderations, to provide an efficient and effective technique that maybe used in wire diagnostics. It may be desirable that this techniqueprovides for diagnosing and detecting faults that may not be detectedusing visual inspection. It may also be desirable that this techniqueprovides for detection as early as possible and perform the diagnosticsin a non-destructive manner that may be included in a routinemaintenance plan.

SUMMARY OF THE INVENTION

According to the present invention, determining an event on a wireincludes receiving a signal on the wire, performing compensationprocessing of the signal producing a compensated signal, performingevent identification processing of the compensated signal to identify atleast one event, and classifying the at least one event. Determiningevents on a wire may also include compensating the signal to removeunwanted reflective components due to inverse scattering producing afirst adjusted signal, and performing attenuation compensation on thefirst adjusted signal. The attenuation compensation may be a function offrequency and an amount of time the signal has traveled in the wire ormay be a function of frequency. Determining events on a wire may alsoinclude associating event data with at least one predetermined eventprior to the classifying, where the classifying uses the event data. Theat least one predetermined event may include at least one of: aconnector, a cut, a nick, a crimp, damage to wire insulation due to age,damage to wire insulation due to coupling of the wire with anotherelement. Determining events on a wire may also include determining theevent data by empirical analysis. Determining events on a wire may alsoinclude determining the event data using a model. Determining events ona wire may also include storing the event data in a library. Determiningevents on a wire may also include determining a first derivative of thesignal and identifying at least one peak of the first derivativeexceeding a predetermined threshold as an event. Determining events on awire may also include determining a plurality of polynomials, each ofthe polynomials locally fitted to a portion of data points defining aportion of the signal, each of the portion of data points beingincluding a kernel point, determining a plurality of first derivativesof the first polynomials, evaluating each of the plurality of firstderivatives at a corresponding kernel point producing a plurality ofevaluated first derivatives, and determining the at least one eventusing the plurality of evaluated first derivatives. The signal may be areflective signal and determining events on a wire may also includeanalyzing the reflective signal in accordance with at least one jointtime-frequency domain reflectometry technique. Determining events on awire may also include sending a signal on the wire where the signal isone of: an impulse signal and a predetermined wavelet. Determiningevents on a wire may also include determining at least onecharacteristic of the reflective signal in accordance with apredetermined wavelet, and using the at least one characteristic in theevent identification and the classifying.

According further to the present invention, a device that determines anevent on a wire includes a receiver that receives a signal on the wireand a processor that performs compensation processing of the signalproducing a compensated signal, performs event identification processingof the compensated signal to identify at least one event, and thatclassifies the at least one event. The processor may compensate thesignal to remove unwanted reflective components due to inversescattering producing a first adjusted signal and performs attenuationcompensation on the first adjusted signal. The attenuation compensationmay be a function of frequency and an amount of time the signal hastraveled in the wire or a function of frequency. The device thatdetermines an event on a wire may also include a data storage elementcontaining event data, where the processor associates the event datawith at least one predetermined event prior to the classifying, wherethe classifying uses the event data. At least one predetermined eventmay include at least one of: a connector, a cut, a nick, a crimp, damageto wire insulation due to age, damage to wire insulation due to couplingof the wire with another element. The processor may determine the eventdata by empirical analysis or by using a model. The processor maydetermine a first derivative of the signal and may identify at least onepeak of the first derivative exceeding a predetermined threshold as anevent. The processor may determine a plurality of polynomials, each ofthe polynomials locally fitted to a portion of data points defining aportion of the signal, each of the portion of data points beingincluding a kernel point, the processor may determine a plurality offirst derivatives of the first polynomials, the processor may evaluateeach of the plurality of first derivatives at a corresponding kernelpoint producing a plurality of evaluated first derivatives, and theprocessor may determine the at least one event using the plurality ofevaluated first derivatives. The signal may be a reflective signal andthe processor may analyze the reflective signal in accordance with atleast one joint time-frequency domain reflectometry technique. Thedevice that determines an event on a wire may also include a signalgenerator that generates at least one of: an impulse signal and apredetermined wavelet. The processor may determine at least onecharacteristic of the reflective signal in accordance with apredetermined wavelet where the at least one characteristic may be usedin the event identification and the classifying.

According further to the present invention, a computer program productthat determines an event on a wire, includes executable code thatreceives a signal on the wire, executable code that performscompensation processing of the signal producing a compensated signal,executable code that performs event identification processing of thecompensated signal to identify at least one event, and executable codethat classifies the at least one event. The computer program product mayalso include executable code that compensates the signal to removeunwanted reflective components due to inverse scattering producing afirst adjusted signal and executable code that performs attenuationcompensation on the first adjusted signal. The attenuation compensationmay be a function of frequency and an amount of time the signal hastraveled in the wire or may be a function of frequency. The computerprogram product may also include executable code that associates eventdata with at least one predetermined event prior to classifying, whereclassifying uses the event data. The at least one predetermined eventmay include at least one of: a connector, a cut, a nick, a crimp, damageto wire insulation due to age, damage to wire insulation due to couplingof the wire with another element. The computer program product may alsoinclude executable code that determines the event data by empiricalanalysis. The computer program product may also include executable codethat determines the event data using a model. The computer programproduct may also include executable code stores the event data in alibrary. The computer program product may also include executable codethat determines a first derivative of the signal and executable codethat identifies at least one peak of the first derivative exceeding apredetermined threshold as an event. The computer program product mayalso include executable code that determines a plurality of polynomials,each of the polynomials locally fitted to a portion of data pointsdefining a portion of the signal, each of the portion of data pointsbeing including a kernel point, executable code that determines aplurality of first derivatives of the first polynomials, executable codethat evaluates each of the plurality of first derivatives at acorresponding kernel point producing a plurality of evaluated firstderivatives, and executable code that determines the at least one eventusing the plurality of evaluated first derivatives. The signal may be areflective signal and the computer program product may also includeexecutable code that analyzes the reflective signal in accordance withat least one joint time-frequency domain reflectometry technique. Thecomputer program product may also include executable code that sends asignal on the wire where the signal is one of: an impulse signal and apredetermined wavelet. The computer program product may also includeexecutable code that determines at least one characteristic of thereflective signal in accordance with a predetermined wavelet, andexecutable code that uses the at least one characteristic in the eventidentification and the classifying.

According further to the present invention, identifying an event ofinterest in a cable includes receiving a voltage waveform signal, takinga first derivative of the voltage waveform signal with respect to time,calculating a standard deviation of a first derivative of system noise,establishing an event detection threshold corresponding to the standarddeviation of the first derivative of system noise, and identifying aportion of the voltage waveform signal having a differential voltagepeak with an absolute value that exceeds the event detection threshold.Identifying an event of interest in a cable may also include convertingthe portion of the voltage waveform signal to a reflection waveformpattern. The system noise may follow a Gaussian distribution.Identifying an event of interest in a cable may also include storing theportion of the voltage waveform signal. Identifying an event of interestin a cable may also include establishing a new event detectionthreshold. The voltage waveform signal received may be corrected forattenuation loss and/or corrected to remove inverse scatteringreflections.

According further to the present invention, a device that identifies anevent of interest in a cable includes a receiver that receives a voltagewaveform signal and a processor that processes the voltage waveformsignal, establishes an event detection threshold corresponding to astandard deviation of a first derivative of system noise, and identifiesa portion of the voltage waveform signal having a differential voltagepeak with an absolute value exceeding the event detection threshold. Theprocessor may convert the portion of the voltage waveform signal into areflection waveform pattern. The device that identifies an event ofinterest in a cable may also include a storage component that stores theportion of the voltage waveform signal.

According further to the present invention, a computer program productthat identifies an event of interest in a cable includes executable codethat receives a voltage waveform signal, executable code that takes afirst derivative of the voltage waveform signal with respect to time,executable code that calculates a standard deviation of a firstderivative of system noise, executable code that establishes an eventdetection threshold corresponding to the standard deviation of the firstderivative of system noise, and executable code that identifies aportion of the voltage waveform signal having a differential voltagepeak with an absolute value that exceeds the event detection threshold.The computer program product may also include executable code thatconverts the portion of the voltage waveform signal to a reflectionwaveform pattern. The system noise may follow a Gaussian distribution.The computer program product may also include executable code thatstores the portion of the voltage waveform signal. The computer programproduct may also include executable code that establishes a new eventdetection threshold. The voltage waveform signal may be corrected forattenuation loss. The voltage waveform signal may be corrected to removeinverse scattering reflections.

According further to the present invention, creating a classificationlibrary for cable analysis includes generating a reflection waveformpattern of an event, processing the reflection waveform pattern toproduce a classification reflection waveform pattern, and storing theclassification reflection waveform pattern. The event may be selectedfrom the group consisting of: a fault, a connector, and a termination.Generating a reflection waveform pattern may include creating aspecified type of fault in a cable of a specified type, producing avoltage waveform signal in the cable, identifying a reflected voltagewaveform signal portion for the specified type of fault, and convertingthe reflected voltage waveform signal portion into a reflection waveformpattern. Generating a reflection waveform pattern may also includesimulating the event utilizing an analytical model and generating areflection waveform pattern from the analytical model. Processing thereflection waveform pattern may includes normalizing and correcting thereflection waveform pattern to produce the classification reflectionwaveform pattern. Creating a classification library for cable analysismay also include providing a plurality of voltage waveform signals,calculating a mean value reflection waveform pattern from at least twonormalized and corrected reflection waveform patterns, calculating avariance array that includes variance information of the least twonormalized reflection waveform patterns compared with the mean valuereflection waveform pattern, and storing the variance array so as to beaccessible with the classification reflection waveform pattern. Creatinga classification library for cable analysis may also include generatinga covariance matrix using information in the variance array and storingthe covariance matrix so as to be accessible with the classificationreflection waveform pattern. Creating a classification library for cableanalysis may also include adjusting component values of the analyticalmodel prior to resimulating the event utilizing an analytical model andregenerating a reflection waveform pattern from the analytical model,generating a variance array corresponding to the adjustment of thecomponent values in the analytical model, and storing the variance arrayso as to be accessible with the classification reflection waveformpattern.

According further to the present invention, a computer program productthat creates a classification library for cable analysis includesexecutable code that generates a reflection waveform pattern of anevent, executable code that processes the reflection waveform pattern toproduce a classification reflection waveform pattern, and executablecode that stores the classification reflection waveform pattern. Theevent may be selected from the group consisting of: a fault, aconnector, and a termination. The executable code that generates areflection waveform pattern of an event may include executable code thatproduces a voltage waveform signal in the cable, executable code thatidentifies a reflected voltage waveform signal portion for a specifiedtype of fault, and executable code that converts the reflected voltagewaveform signal portion into a reflection waveform pattern. Theexecutable code that generates a reflection waveform pattern of an eventmay include executable code that simulates the event utilizing ananalytical model and executable code that generates a reflectionwaveform pattern from the analytical model. The executable code thatprocesses the reflection waveform pattern to produce a classificationreflection waveform pattern may include executable code that normalizesand corrects the reflection waveform pattern to produce theclassification reflection waveform pattern. The computer program productmay also include executable code that calculates a mean value reflectionwaveform pattern from at least two normalized and corrected reflectionwaveform patterns, executable code that calculates a variance array thatincludes variance information of the least two normalized reflectionwaveform patterns compared with the mean value reflection waveformpattern, and executable code that stores the variance array so as to beaccessible with the classification reflection waveform pattern. Thecomputer program product may also include executable code that generatesa covariance matrix using information in the variance array, andexecutable code that stores the covariance matrix so as to be accessiblewith the classification reflection waveform pattern. The computerprogram product may also include executable code that adjusts componentvalues of the analytical model, executable code that generates avariance array corresponding to the adjustment of the component valuesin the analytical model, and executable code that stores the variancearray so as to be accessible with the classification reflection waveformpattern.

According further to the present invention, compensating an electricalsignal includes digitizing the electrical signal to provide a digitizedsignal, determining attenuation as a function of signal frequency,constructing a digital filter that approximates an inverse of theattenuation, and applying the digital filter to the digitized signal.Determining attenuation as a function of frequency may include using theequation: A(f, L)=e^(−(R (f)*L/Z0)), where Z0 is the characteristicimpedance of a conductor on which the electrical signal propagates, L isthe length of the conductor, and R(f) is the frequency dependentresistance of the conductor. R(f) may be proportional to the square rootof the frequency. R(f) may be determined using the equation: R(f)=(½r)*(μf/πσ)^(1/2), where r is the radius of the conductor, μ is thepermeability of free space in henries per meter, and σ is theconductivity of material of the conductor. The value of σ may be 5.8×10⁷ohms/meter. Compensating an electrical signal may also includedetermining length of the conductor. Determining the length of theconductor may also include taking a derivative of the digitized signal,determining if the conductor terminates in one of: an open and a short,if the conductor terminates in an open, finding the maximum value forthe derivative and calculating the length based thereon, and if theconductor terminates in a short, finding a minimum value for thederivative and calculating the length based thereon. Compensating anelectrical signal may also include determining a median voltage betweena first one of the digitized signals and a digitized signalcorresponding to the length of the conductor. Compensating an electricalsignal may also include determining the impedance of the conductor basedon the median voltage. The attenuation may also be a function of alength traveled by each portion of the signal and varies as a functionof time. Determining attenuation as a function of frequency may includeusing the equation: A(f, L)=e^(−(R (f)*L/Z0)), where Z0 is thecharacteristic impedance of a conductor on which the electrical signalpropagates, L is proportional to a time of sampling of the digitizedsignal, and R(f) is the frequency dependent resistance of the conductor.Coefficients of the digital filter may vary according to the time ofsampling of the digitized signal. Compensating an electrical signal mayalso include determining length of the conductor. Determining the lengthof the conductor may also include taking a derivative of the digitizedsignal, determining if the conductor terminates in one of: an open and ashort, if the conductor terminates in an open, finding the maximum valuefor the derivative and calculating the length based thereon, and if theconductor terminates in a short, finding a minimum value for thederivative and calculating the length based thereon. Compensating anelectrical signal may also include determining a median voltage betweena first one of the digitized signals and a digitized signalcorresponding to the length of the conductor. Compensating an electricalsignal may also include determining the impedance of the conductor basedon the median voltage. The digital filter may be an FIR filter.

According further to the present invention, a computer program productthat compensates an electrical signal includes executable code thatdigitizes the electrical signal to provide a digitized signal,executable code that determines attenuation as a function of signalfrequency, constructing a digital filter that approximates an inverse ofthe attenuation, and applying the digital filter to the digitizedsignal. Executable code that determines attenuation as a function offrequency may use the equation: A(f, L)=e^(−(R (f)*L/Z0)), where Z0 isthe characteristic impedance of a conductor on which the electricalsignal propagates, L is the length of the conductor, and R(f) is thefrequency dependent resistance of the conductor. R(f) may beproportional to the square root of the frequency. R(f) may be determinedusing the equation: R(f)=(½r)* (μf/πσ)^(1/2), where r is the radius ofthe conductor, μ is the permeability of free space in henries per meter,and σ is the conductivity of material of the conductor. The value of σmay be 5.8×10⁷ ohms/meter. The computer program product may also includeexecutable code that determines length of the conductor. Executable codethat determines the length of the conductor may also include executablecode that takes a derivative of the digitized signal, executable codethat determines if the conductor terminates in one of: an open and ashort, executable code that finds the maximum value for the derivativeand calculates the length based thereon if the conductor terminates inan open, and executable code that finds a minimum value for thederivative and calculates the length based thereon if the conductorterminates in a short. The computer program product may also includeexecutable code that determines a median voltage between a first one ofthe digitized signals and a digitized signal corresponding to the lengthof the conductor. The computer program product may also includeexecutable code that determines the impedance of the conductor based onthe median voltage. The attenuation may also be a function of a lengthtraveled by each portion of the signal and varies as a function of time.Executable code that determines attenuation as a function of frequencymay use the equation: A(f, L)=e^(−(R (f) *L/Z0)), where Z0 is thecharacteristic impedance of a conductor on which the electrical signalpropagates, L is proportional to a time of sampling of the digitizedsignal, and R(f) is the frequency dependent resistance of the conductor.Coefficients of the digital filter may vary according to the time ofsampling of the digitized signal. The computer program product may alsoinclude executable code that determines length of the conductor.Executable code that determines the length of the conductor may includeexecutable code that takes a derivative of the digitized signal,executable code that determines if the conductor terminates in one of:an open and a short, executable code that finds the maximum value forthe derivative and calculates the length based thereon if the conductorterminates in an open, and executable code that finds a minimum valuefor the derivative and calculates the length based thereon if theconductor terminates in a short. The computer program product may alsoinclude executable code that determines a median voltage between a firstone of the digitized signals and a digitized signal corresponding to thelength of the conductor. The computer program product may also includeexecutable code that determines the impedance of the conductor based onthe median voltage. The digital filter may be an FIR filter.

According further to the present invention, classifying a portion of anelectrical signal propagating through a conductor, includes digitizingthe electrical signal to provide a digitized signal, providing aplurality of stored digitized signals, where each stored digitizedsignal corresponds to a type of fault for the conductor, determining aplurality of scores by comparing the digitized signal with each of theplurality of stored signals, selecting a highest one of the scores,classifying the portion of the signal according to a type of faultcorresponding to the highest one of the scores if the highest one of thescores is greater than a predetermined value, and classifying theportion of the electrical signal as noise if the highest one of thescores is not greater than the predetermined value. Classifying aportion of an electrical signal may also include converting thedigitized signal to reflection coefficients. The reflection coefficientsmay correspond to values of the digitized signal divided by an inputsignal magnitude. Determining a plurality of scores may includeobtaining variance values for each of the stored digitized signals,obtaining a stored digitized signal corresponding to noise, andcalculating each of the scores using the digitized signal, the variancevalues, the stored digitized signal corresponding to noise, and each ofthe stored digitized signals corresponding to each type of fault.Determining a plurality of scores may include obtaining variance valuesfor each of the stored digitized signals, obtaining covariance valuesfor each of the stored digitized signals, obtaining a stored digitizedsignal corresponding to noise, and calculating each of the scores usingthe digitized signal, the variance values, the covariance values, thestored digitized signal corresponding to noise, and each of the storeddigitized signals corresponding to each type of fault. The variance andcovariance values may be provided in a matrix.

According further to the present invention, a computer program productthat classifies a portion of an electrical signal propagating through aconductor, includes executable code that digitizes the electrical signalto provide a digitized signal, executable code that provides a pluralityof stored digitized signals, where each stored digitized signalcorresponds to a type of fault for the conductor, executable code thatdetermines a plurality of scores by comparing the digitized signal witheach of the plurality of stored signals, executable code that selects ahighest one of the scores, executable code that classifies the portionof the signal according to a type of fault corresponding to the highestone of the scores if the highest one of the scores is greater than apredetermined value, and executable code that classifies the portion ofthe electrical signal as noise if the highest one of the scores is notgreater than the predetermined value. The computer program may alsoinclude executable code that converts the digitized signal to reflectioncoefficients. The reflection coefficients may correspond to values ofthe digitized signal divided by an input signal magnitude. Executablecode that determines a plurality of scores may include executable codethat obtains variance values for each of the stored digitized signals,executable code that obtains a stored digitized signal corresponding tonoise, and executable code that calculates each of the scores using thedigitized signal, the variance values, the stored digitized signalcorresponding to noise, and each of the stored digitized signalscorresponding to each type of fault. Executable code that determines aplurality of scores may include executable code that obtains variancevalues for each of the stored digitized signals, executable code thatobtains covariance values for each of the stored digitized signals,executable code that obtains a stored digitized signal corresponding tonoise, and executable code that calculates each of the scores using thedigitized signal, the variance values, the covariance values, the storeddigitized signal corresponding to noise, and each of the storeddigitized signals corresponding to each type of fault. The variance andcovariance values may be provided in a matrix.

According further to the present invention, detecting an event on a wireincludes determining a plurality of polynomials, each of the polynomialsfitting a portion of data points representing a received waveform,determining a first derivative for each of the plurality of polynomials,evaluating the first derivative of each of the plurality of polynomialsat data points representing the received waveform, and detecting anevent using the first derivative of each of the plurality ofpolynomials. Detecting an event on a wire may also include compensatingthe received waveform prior to the determining a plurality ofpolynomials. The event may be one of: a connector, a cut, a nick, acrimp, damage to wire insulation due to age, damage to wire insulationdue to coupling of the wire with another element. Detecting an event ona wire may also include storing data of the waveform in accordance withthe event detected. Detecting an event on a wire may also includeclassifying the event. The portion of data points may have N+M+1 datapoints, N representing a number of data points prior to a first one ofthe data points included in the portion, M representing a number of datapoints prior to the first one of the data points included in theportion, and detecting an event on a wire may also include determining afirst of the plurality of polynomials in accordance with the N+M+1 datapoints. Detecting an event on a wire may also include determining afirst derivative of the first polynomial and evaluating the firstderivative at the first one of the data points included in the portion.Detecting an event on a wire may also include determining an eventdetection threshold. Detecting an event on a wire may also includedetermining at least one peak using the first derivatives that exceedsthe event detection threshold, storing data corresponding to the atleast one peak, and classifying the data as one of a plurality ofevents.

According further to the present invention, a computer program productfor detecting an event on a wire includes executable code thatdetermines a plurality of polynomials, each of the polynomials fitting aportion of data points representing a received waveform, executable codethat determines a first derivative for each of the plurality ofpolynomials, executable code that evaluates the first derivative of eachof the plurality of polynomials at data points representing the receivedwaveform, and executable code that detects an event using the firstderivative of each of the plurality of polynomials. The computer programproduct may also include executable code that compensates the receivedwaveform prior to the determining a plurality of polynomials. The eventmay be one of: a connector, a cut, a nick, a crimp, damage to wireinsulation due to age, damage to wire insulation due to coupling of thewire with another element. The computer program product may also includeexecutable code that stores data of the waveform in accordance with theevent detected. The computer program product may also include executablecode that classifies the event. The portion of data points may haveN+M+1 data points, N representing a number of data points prior to afirst one of the data points included in the portion, M representing anumber of data points prior to the first one of the data points includedin the portion, and the computer program product further includingexecutable code that determines a first of the plurality of polynomialsin accordance with the N+M+1 data points. The computer program productmay also include executable code that determines a first derivative ofthe first polynomial and executable code that evaluates the firstderivative at the first one of the data points included in the portion.The computer program product may also include executable code thatdetermines an event detection threshold. The computer program productmay also include executable code that determines at least one peak usingthe first derivatives evaluated that exceed the event detectionthreshold, executable code that stores data corresponding to the atleast one peak, and executable code that classifies the data as one of aplurality of events.

According further to the present invention, processing a signal receivedon a wire includes receiving the signal, compensating the signal toremove unwanted reflections caused by a defect in the wire producing acompensated signal, and analyzing the compensated signal to determineinformation about the defect. Processing a signal received on a wire mayalso include receiving a plurality of reflective voltages and aplurality of incident voltages, where at a measured voltage at a time isequal to a sum of a reflective voltage and an incident voltage at a thetime and adjusting each of the plurality of reflective voltages and theplurality of incident voltages determined at a point to remove unwantedreflections from the point to the end of the wire. There may be Nincident voltages and N corresponding reflective voltages, andprocessing a signal received on a wire may also include initializing afirst row of an N×N matrix, D, with the N incident voltages,initializing a first row of an N×N matrix, U, with the N reflectivevoltages, determining reflection coefficients corresponding to the Nincident and N reflective voltages, determining transmissioncoefficients corresponding to the reflection coefficients, for eachelement of row ii of matrix D, ii=2 to N, determiningD(ii,jj)=(D(i,j)−r(ii)*U(i, jj))/s(ii), where i=1 to N−1, j=i to N−1,jj=j+1, s(ii) is a transmission coefficient at time ii, r(ii) is areflection coefficient at a time ii, and for each element of row ii ofmatrix U, determining U(ii,jj)=(−r(ii)*D(i,j)+U(i,jj))/s(ii), wherediagonals of matrix D, D[t,t], t=1 to N, are N adjusted incidentvoltages at each time t, Vinc,adj(t). Processing a signal received on awire may also include determining adjusted reflective voltages at eachtime t, Vrefl,adj(t), as:Vrefl,adj(t)=(Z(t+1)−Z₀)/(Z₀+Z(t+1))*Vinc,adj(t)+Vinc,adj(t), where Z₀is a characteristic impedance of the wire,Z(t+1)=Z(t)*(1+r(t))/(1−r(t)). Processing a signal received on a wiremay also include performing error correction by assigning each of thereflection coefficients to zero if the each reflection coefficient isless than a predetermined threshold. The predetermined threshold may bea value equal to a product of three times a standard deviation of anoise level.

According further to the present invention, a computer program productthat processes a signal received on a wire includes executable code thatreceives the signal, executable code that compensates the signal toremove unwanted reflections caused by a defect in the wire producing acompensated signal, and executable code that analyzes the compensatedsignal to determine information about the defect. The computer programproduct may also include executable code that receives a plurality ofreflective voltages and a plurality of incident voltages, where at ameasured voltage at a time is equal to a sum of a reflective voltage andan incident voltage at a the time and executable code that adjusts eachof the plurality of reflective voltages and the plurality of incidentvoltages determined at a point to remove unwanted reflections from thepoint to the end of the wire. There may be N incident voltages and Ncorresponding reflective voltages, and the computer program product mayfurther executable code that initializes a first row of an N×N matrix,D, with the N incident voltages, executable code that initializes afirst row of an N×N matrix, U, with the N reflective voltages,executable code that determines reflection coefficients corresponding tothe N incident and N reflective voltages, executable code thatdetermines transmission coefficients corresponding to the reflectioncoefficients, executable code that, for each element of row ii of matrixD, ii=2 to N, determines D(ii,jj)=(D(i,j)−r(ii)*U(i, jj))/s(ii), wherei=1 to N−1,j=i to N−1, jj=j+1, s(ii) is a transmission coefficient attime ii, r(ii) is a reflection coefficient at a time ii; and executablecode that, for each element of row ii of matrix U, determinesU(ii,jj)=(−r(ii)*D(i,j)+U(i,jj))/s(ii), where diagonals of matrix D,D[t,t], t=1 to N, are N adjusted incident voltages at each time t,Vinc,adj(t). The computer program product may also include executablecode that determines adjusted reflective voltages at each time t,Vrefl,adj(t), as:Vrefl,adj(t)=(Z(t+1)−Z₀)/(Z₀+Z(t+1))*Vinc,adj(t)+Vinc,adj(t), where Z₀is a characteristic impedance of the wire, Z(t+1)=Z(t)*(1+r(t))/(1−r(t)). The computer program product may also includeexecutable code that performs error correction by assigning each of thereflection coefficients to zero if the each reflection coefficient isless than a predetermined threshold. The predetermined threshold may bea value equal to a product of three times a standard deviation of anoise level.

According further to the present invention, detecting events on a wireincludes determining at least one set of reference data indicating awire event, sending an impulse signal on the wire, obtaining areflective return signal corresponding to the impulse signal, andanalyzing the reflective signal in accordance with at least one jointtime-frequency domain reflectometry technique. The impulse signal may begenerated in accordance with a predetermined wavelet. Detecting eventson a wire may also include determining at least one characteristic ofthe reflective signal in accordance with a predetermined wavelet.Detecting events on a wire may also include performing wavelet analysisusing a continuous wavelet transform. Detecting events on a wire mayalso include determining ρ as a feature of the reflective signal where ρis a differential wavelet energy ratio ρ proportional to the deviationof a signature energy with respect to a baseline of a the wire in ahealthy condition for a given time-frequency span. Increasing values ofρ, may be associated with increasing severity of wire events detected.The value of ρ may be represented as:

$\rho = \sqrt{\frac{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{{C_{sk} - C_{sk}^{Baseline}}}^{2}}}{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{C_{sk}^{Baseline}}^{2}}}}$in which C_(sk) represents continuous wavelet coefficients of a signalunder test collected over a time-span of N samples and a time-scale spanof S scales, where the scales are parameters used in performing thewavelet analysis and C_(sk) ^(Baseline) represents a set of waveletcoefficients of a baseline signal associated with a healthy signature.Detecting events on a wire may also include determining δ as a featureof the reflective signal, where δ is a local wavelet energy ratio of asignature of interest with respect to a baseline of a healthy signature,the local nature of the signatures relating to a partial derivative ofsignal energy with respect to a time-scale corresponding to an inversefrequency of the signal energy. The value of δ may be represented as:

$\delta = \sqrt{\frac{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{{\frac{\partial C_{sk}}{\partial s} - \frac{\partial C_{sk}^{Baseline}}{\partial s}}}^{2}}}{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{\frac{\partial C_{sk}^{Baseline}}{\partial s}}^{2}}}}$in which ∂ represents a partial derivative. Detecting events on a wiremay also include decomposing the reflective signal. The reflectivesignal may be decomposed into at least one intrinsic mode function.Detecting events on a wire may also include applying a Hilbert transformto each of the at least one intrinsic mode function.

According further to the present invention, detecting events on a wireincludes determining at least one set of reference data indicating awire event, sending an impulse signal on the wire, obtaining areflective return signal corresponding to the impulse signal, andanalyzing the reflective signal producing at least one jointtime-frequency parameter. Detecting events on a wire may also includedetermining an occurrence of a wire event by comparing values of the atleast one joint time-frequency parameter of the wire to known parametervalues associated with the wire event. Detecting events on a wire mayalso include performing at least one of: a wavelet analysis and aHilbert-Huang transform when analyzing the reflective signal.

According further to the present invention, a computer program productfor detecting events on a wire includes executable code that determinesat least one set of reference data indicating a wire event, executablecode that sends an impulse signal on the wire, executable code thatobtains a reflective return signal corresponding to the impulse signal,and executable code that analyzes the reflective signal in accordancewith at least one joint time-frequency domain reflectometry technique.The impulse signal may be generated in accordance with a predeterminedwavelet. The computer program product may include executable code thatdetermines at least one characteristic of the reflective signal inaccordance with a predetermined wavelet. The computer program productmay include executable code that performs wavelet analysis using acontinuous wavelet transform. The computer program product may includeexecutable code that determines ρ as a feature of the reflective signalwhere ρ is a differential wavelet energy ratio ρ proportional to thedeviation of a signature energy with respect to a baseline of a the wirein a healthy condition for a given time-frequency span. Increasingvalues of ρ, may be associated with increasing severity of wire eventsdetected. The value of ρ may be represented as:

$\rho = \sqrt{\frac{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{{C_{sk} - C_{sk}^{Baseline}}}^{2}}}{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{C_{sk}^{Baseline}}^{2}}}}$in which C_(sk) represents continuous wavelet coefficients of a signalunder test collected over a time-span of N samples and a time-scale spanof S scales, where the scales are parameters used in performing thewavelet analysis and C_(sk) ^(Baseline) represents a set of waveletcoefficients of a baseline signal associated with a healthy signature.The computer program product may include executable code that determinesδ as a feature of the reflective signal, where δ is a local waveletenergy ratio of a signature of interest with respect to a baseline of ahealthy signature, the local nature of the signatures relating to apartial derivative of signal energy with respect to a time-scalecorresponding to an inverse frequency of the signal energy. The value ofδ may be represented as:

$\delta = \sqrt{\frac{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{{\frac{\partial C_{sk}}{\partial s} - \frac{\partial C_{sk}^{Baseline}}{\partial s}}}^{2}}}{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{\frac{\partial C_{sk}^{Baseline}}{\partial s}}^{2}}}}$in which ∂ represents a partial derivative. The computer program productmay include machine executable code that decomposes the reflectivesignal. The reflective signal may be decomposed into at least oneintrinsic mode function. The computer program product may includemachine executable code that applies a Hilbert transform to each of theat least one intrinsic mode function.

According further to the present invention, a computer program productfor detecting events on a wire includes executable code that determinesat least one set of reference data indicating a wire event, executablecode that sends an impulse signal on the wire, executable code thatobtains a reflective return signal corresponding to the impulse signal,and executable code that analyzes the reflective signal producing atleast one joint time-frequency parameter. The computer program productmay include executable code that determines an occurrence of a wireevent by comparing values of the at least one joint time-frequencyparameter of the wire to known parameter values associated with the wireevent. The computer program product may include machine executable codethat performs at least one of: a wavelet analysis and a Hilbert-Huangtransform when analyzing the reflective signal.

BRIEF DESCRIPTION OF DRAWINGS

Features and advantages of the present invention will become moreapparent from the following detailed description of exemplaryembodiments thereof taken in conjunction with the accompanying drawingsin which:

FIG. 1 is an example of an embodiment of a system according to thepresent invention;

FIG. 2 is an example of a dataflow diagram of the various processingcomponents that may be used in the system of FIG. 1;

FIG. 3 is a flowchart of steps of an embodiment for processing receivedsignals within the system of FIG. 1;

FIG. 4 is a flowchart of steps of an embodiment for compensatingreceived signals to remove unwanted reflective components due to theinverse scattering phenomena;

FIG. 5A is a graphical illustration of one embodiment of how theunwanted reflective components removed may appear in a waveform;

FIG. 5B is another graphical illustration of how the unwanted reflectivecomponents and reflective components related to wire events may appearin a waveform;

FIG. 6 is a graphical illustration of one embodiment of the inversescattering problem and the associated reflective artifacts;

FIG. 7 is a flowchart showing steps for attenuation compensation.

FIG. 8 is a flowchart showing steps for determining the length andcharacteristic impedance of a cable.

FIG. 9A is a flowchart showing steps for identifying events with acontrolled false alarm rate according to one embodiment.

FIG. 9B is a flowchart showing steps for identifying events with acontrolled false alarm rate according to another embodiment.

FIG. 9C is a flowchart showing in more detail processing for determiningevents of interest.

FIG. 10 is a flowchart showing in more detail the processing where eachof the events are classified.

FIG. 11 is a flowchart showing the calculation of the score for each ofthe faults in the fault library.

FIG. 12 is a flowchart showing a more generalized calculation forcalculating the values for score[j] that takes into account thecovariance.

FIG. 13A is an example of a test signal on a cable in which the signalis averaged and variance calculated on the returns and showingidentified events of interest.

FIG. 13B is an example of a display showing classification and distanceinformation for the identified events after pattern matching and otherprocessing according to one embodiment of the invention.

FIG. 14 is a schematic illustration of a general GRLC cable model of anincremental length Δx.

FIG. 15 is a schematic illustration of a model RL series-type mismatch.

FIG. 16 illustrates a typical time response of an RL series-typemismatch.

FIG. 17 illustrates a typical time response of an RC parallel-typemismatch.

FIG. 18 illustrates a typical time response of an RL parallel-typemismatch.

FIG. 19 illustrates the generated reflection coefficient (rho (ρ))values for event types as stored in the fault library.

FIG. 20 is an example of an embodiment of a system used for jointtime-frequency domain reflectometry(TFDR);

FIG. 21 is a more detailed configuration of an embodiment of FIG. 20;

FIG. 22A is an example of an embodiment of a software interface;

FIG. 22B is a flowchart of method steps of one embodiment for performingTFDR techniques to identify wire events;

FIG. 22C is a flowchart of methods steps of one embodiment to gatherdata about wire events and a healthy wire;

FIG. 23 is an illustration of a cable inflicted with abrasions anddamage as measured in processing steps of FIG. 22C;

FIGS. 24A-24G are illustrations of different defects in one embodimentfor which data is gathered and used for comparison to data for a wireunder test;

FIG. 24H is a graphical illustration of reflections generated by aneight ns-width pulse and samples at 1-GHZ frequency;

FIG. 25 is a graphical illustration of the variation of the differentialwavelet energy ratio versus the fault conditions of FIGS. 24A-24G;

FIG. 26A is a graphical illustration of the local wavelet energy ratioversus the fault conditions of FIGS. 24A-24G;

FIG. 26B is a flowchart of steps of one embodiment summarizing thewavelet TFDR technique;

FIG. 26C is a flowchart of steps of one embodiment summarizing the HHTTFDR technique;

FIGS. 27A-27D are graphical illustrations of the a voltage signature andits decomposed 11 intrinsic mode functions (IMFs);

FIG. 28A is a graphical illustration of a measured reflected signal;

FIG. 28B is a graphical illustration of the Fourier-based spectrum usingthe signal from FIG. 28A;

FIG. 28C is a graphical illustration of the wavelet transform using thesignal from FIG. 28A;

FIG. 28D is a graphical illustration of the Hilbert-Huang Transformusing the signal from FIG. 28A.

DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS

Referring to FIG. 1, shown is a system 40 that performs wirediagnostics. The system 40 includes a pin connection 42 that couples toone or more pins of a wire that may be part of a wiring harness. The pinconnection 42 may connect to a single pin or may connect to multiplepins. In some instances (described elsewhere herein), a signal isgenerated and provided on a first pin and signal is received on asecond, different pin. In other embodiments, a signal is generated on apin and a signal is measured on the same pin. The sent and receivedsignals are provided through the pin connection 42.

A signal generator 44 is coupled to the pin connection 42 and provides asignal thereto. In some embodiments, the signal generator 44 may providea square pulse or step function pulse. In other embodiments, the signalgenerator 44 may provide a swept frequency signal or may provide a sinewave at a particular frequency or at a particular set of frequencies.Much, if not all, of the analysis described herein can be extended to beapplicable to any type of excitation signal beside a square or steppulse.

Signals sensed at the pin connection 44 are provided to a signalreceiver 46. The signal receiver 46 may digitize the signal and/or mayotherwise condition the received signal to facilitate further onprocessing.

The output of the signal receiver 46 is provided to a processor 48 whichmay be any commercially available processor suitable for providing thefunctionality described herein including, without limitation, any one ofa variety of hand-held, notebook, or desktop computers. The processor 48may also provide an input to the signal generator 44. In someembodiments, the processor 48 may trigger the single generator 44. Inother embodiments, the processor 48 may indicate to the signal generator44 one of a plurality of signals to be generated. Alternatively still,the processor 48 may provide a digital signal to be generated and thesignal generator 44 may convert the digital signal to an analog signalprior to providing the signal to the pin connection 42.

A data storage element 52 may contain data that is used by the processor48 for processing the signals. Data stored in the data storage element52 may include prior signals (i.e., signals from previous iterations) aswell as a library of particular signals that are used to analyze thesignals received by the signal receiver 46, as described elsewhereherein. In some embodiments, the signal receiver 46 may store thecurrent signal in the data storage data element 52 so that the storagedata element 52 contains the current signal as well as signals fromprevious iterations that may be provided to the processor 48.

As described herein, the processor 48 processes the received signal,possibly the prior signals, and possibly the library of signals (andpossibly other data) to identify events and output results in accordancewith the detected event. As described elsewhere herein, an event may bea connector, or some type of fault. There can be different types offaults such as hard faults and soft faults. Hard faults include, forexample, shorts and incorrect types of terminations within the wire.Soft faults include, for example, opens, inductive faults and capacitivefaults. A soft fault may not require maintenance. However, maintenancemay be required if and when a soft fault changes in one or moredifferent aspects. For example, a soft fault may progress over time andbecome more serious or may move. The data storage element 52, as alsodescribed herein in more detail, may include information used indetecting the occurrence of the event and how it may also change overtime. The foregoing allows for an embodiment to use a condition-basedapproach in which not only can events be detected, but changes in eventsover time may be examined. Such changes may be useful, for example, inscheduling maintenance.

Results may indicate, for example, if a wire being tested has a faultand the type/location of the fault. The possible options for the resultare described elsewhere herein. Note that the result may be provided toa user display to display the result to the user and/or may be providedto storage that is accessed later and/or may be provided to some othertype of indicator (such as an LED) that indicates, for example, that awire fault has been detected.

The functionality of the system 40 may be provided using any one of avariety of commercially-available measurement/generation systems aloneor in combination with components provided by a user. For example, highperformance oscilloscopes marketed by Tektronix, Agilent Technologies,and Hewlett Packard might be suitable when used in combination with highfrequency step generators used for the signal generator 44 in connectionwith embodiments where. the signal generator 44 provides a step or pulsewave form. For example, the Tektronix TDS 8000 sampling oscilloscopemight be used to provide at least part of the functionality of thesystem 40. Other companies such a Raser Bond Instrument, BicotestLimited, and Eclipse Industries provide portable test units for testingwires and cables. The signal generator 44 may be provided using a steprecovery diode (SRD) that is commercially provided by the HewlettPackard Company. Other SRD's include a Metelics MMD 830-E28X StepRecovery Diodes. The SRD's may be used with MHS-40,02-G2sX hybridshotkey high conductance diodes. These components may be used toconstruct the signal generator 44 to provide a very fast rise time pulsesignal.

A Compaq PocketPC 400 MHz Processor with 64 MBytes of RAM may be usedfor the processor 48. The PocketPC may be used in connection with a CMTechnologies Company PCMCIA TDR Card for sending/receiving signals. Thealgorithms used by the processor 48 (described elsewhere herein) may beimplemented with Matlab and/or with C++ using the Microsoft Visual C++library with target platform being the Microsoft Windows CE operatingsystem. In one embodiment, machine executable code, as may be producedusing compilers, linkers, and other tools, may be executed by theprocessor 48. The machine executable code may be stored on the datastorage element 52, such as a disk, in read-only-memory, and/or othercomponent of the system 40. It should be noted that other embodimentsmay utilize different hardware and/or software to implement thetechniques described herein and the particulars described herein shouldnot be construed as a limitation.

The system described herein may utilize Time Domain Reflectometry (TDR).TDR may generally be described as the analysis of a conductor, such as awire, cable or fiber optic line, that is performed by sending a pulsedsignal into the conductor and then subsequently examining the reflectedpulse or signal. Wiring and insulation anomalies cause differentcapacitance and inductance to occur in the wire than the nominal wireswhich further causes a change in the local characteristic impedance. Thechange in the characteristic impedance will scatter in the pulsed signalreflecting some part of the signal energy. By measuring the time delay,the precise location of the anomaly may be determined while the polarityof the anomaly may be used to determine the particular type of faultwithin the conductor. TDR measures voltage vs. time.

The system described herein may also utilize Frequency DomainReflectometry (FDR). FDR may generally be characterized as anothertechnique for wire analysis that comprises splitting an input signal toa cable under test and to a mixer and subsequently sending a reflectedinput signal back to the mixer to generate a mixed signal in which thehigh frequency components are removed. The remaining DC componentscontain information regarding the impedance and length of the cableunder test. This operation may be performed a number of times at varyingfrequencies, for example, and the digitized signal may be used todetermine the impedance and length of the cable under test. As describedherein, FDR may be used as an alternative technique to TDR. FDR measuresreal and imaginary parts of a signal vs. frequency.

Impedance may be defined as a relationship of voltage to current and maybe represented as V=ZI where Z is called the impedance of the element.Wires and cables have characteristic impedances relating to the wire'scapacitance per unit length, inductance per unit length and the velocityof signal propagation within the wire. When a defect occurs within awire, for example, the particular wire having the anomaly has adifferent capacitance and inductance than a normal wire which causes achange in the local characteristic impedance. It has been shown thatwhen there is a mismatch in characteristic impedance of a particularwire, some small amount of energy is reflected from the discontinuity.Where there are a number of these mismatches in the characteristicimpedance close to each other on the transmission pass, theirreflections may interact and generate a number of reflective artifacts.

Referring back to FIG. 1, these various reflections may distort ameasured wave form received by the pin connection 42 which is then sentto the signal receiver 46 making analysis of the true impedance of thetransmission path difficult. This particular problem will be referred toherein as the inverse scattering problem. The process of determining thetrue transmission line impedance from a measured wave form, such as inthe form of a received signal, may be accomplished by adjusting orcompensating a received signal value to account for this inversescattering and other noise or interferences. It should be noted thatwhile the inverse scattering phenomena as described herein has beensolved and applied in other fields, such as seismology, as describedherein, the inverse scattering problem is integrated into a wirediagnostic tool for use with techniques described herein.

As applied to the wire diagnostics problem, multiple reflections mayoccur due to one or more faults within a wire. What will be describedherein is a technique that may be used to compensate for theseadditional inverse scattering reflections. By removing this componentfrom the received signals of a measured wave form, the measured waveform may be adjusted and analyzed to a greater degree of accuracy inconnection with determining a particular type and location of a faultwithin a wire.

Referring now to FIG. 2, shown is an example 100 of a dataflow diagramof the various processing components that may be included within thesystem 40 previously described in connection with FIG. 1. The example100 includes a compensation processing component 102, an eventidentification component 104, a parametric classification component 106,an empirical analysis generator component 108, and a fault modelgenerator component 110. Additionally, included is a library 112, whichmay be stored, for example, in the data storage element 52, previouslydescribed in connection with the system 40 of FIG. 1.

In one embodiment, each of the components 102, 104, 106, 108 and 110 maybe implemented, for example, utilizing software as described elsewherehere in more detail to produce machine executable instructions executedby the processor 48. The machine executable instructions may perform thevarious processing steps as described elsewhere herein in more detailfor each of the components included in the example 100 of FIG. 2.

The compensation processing component 102 includes processing steps tocompensate or remove unwanted interference from the received signal,such as a received reflective signal. Compensation may include, forexample, adjusting a received signal to take into account multiplereflections as encountered with the inverse scattering problem.Compensation processing may also include attenuation compensation,described elsewhere herein in more detail, and other types ofcompensation. Once the signal has been compensated, the compensatedsignal is used as input to event identification component processing104. Event identification component processing detects points or eventsof interest. In connection with wire diagnostics system, for example, anevent may be any change in characteristic impedance such as, forexample, a connector, a cut, a nick, a crimp, damage to wire insulationdue to age or coupling with other structures or wires, and the like.

Once an event has been detected by event identification componentprocessing 104, the event or point of interest is then input to aclassification component, such as the parametric classificationcomponent 106. The parametric classification component 106 may uselibrary 112 that includes a set of potential events, such as connectors,terminations, faults such as inductive faults and capacitive faults, andthe like. The parametric classification component 106 examines variousparameters of an input and compares those parameters to valuesassociated with known events as may be stored, for example, in thelibrary 112. Through this comparison, the event may be identified asindicated in output results from the parametric classification component106.

In one embodiment, the library 112 may include sets of potential eventssuch as different types of faults. An inductive fault, for example, mayrelate to damage of wire insulation due to cuts, nicks, and breaks. Theymay be generally characterized as inductive faults because local wireinductance may be larger than the nominal wire resulting in the increasein characteristic impedance. Capacitive faults, for example, may relateto damage characteristics of crimps or bends within a wire where theinsulation is thinned and local capacitance increases. This may cause adrop in the wire characteristic impedance. An event type of atermination may be classified as one of the four basic categories: open,short, inductive short, and capacitive short. An open termination mayreflect a switch or a cut within the wire. A short may reflect atermination to ground and may be immediately characterized as a fault.Inductive shorts and capacitive shorts may reflect various hardwareterminations such as a fuel probe and may be used for faultclassification. In other words, inductive shorts and capacitive shortsmay or may not indicate a problem. For example, for a wire supplying afuel probe, any termination other than a capacitive short may indicate afault.

It should be noted that other types of events may be included andcharacterized in accordance with different known parameter values withinthe library 112. The library 112 may include data that has been storedprior to using the system 40 of FIG. 1 to perform wire diagnostictroubleshooting. At some time prior to executing, for example,processing steps associated with components 102, 104 and 106, thelibrary 112 may be constructed using any one or more of a variety oftechniques. As described herein in more detail, embodiment may use anempirical analysis generator component 108 and a fault model generatorcomponent 110 in order to produce library 112 that includes sets ofpotential events. Components 108 and 110 may be executed to populate thelibrary 112 prior to executing the processing steps of components 102,104 and 106.

The empirical analysis generator component 108 may use actual dataobtained by measuring values in accordance with different types of faultconditions or events. This data may be recorded and stored within thelibrary 112. As an alternative for additional techniques for populatingthe library 112, the fault model generator component 110 may also beutilized. The fault model generator component 110 utilizes modelingtechniques in order to model or simulate conditions to generate data forpopulating the library 112 in accordance with different types of events,such as the foregoing wire events.

It should be noted that an embodiment may utilize other techniques inconnection with populating the library 112 with particular dataassociated with the events to be determined by the parametricclassification or other type of classification system included in anembodiment.

Referring now to FIG. 3, shown is a flowchart 120 of steps of anembodiment for processing received signals within the system 40 ofFIG. 1. At step 122, a signal is received. At step 124, a first type ofsignal compensation processing is performed. As described elsewhereherein in more detail, this is described as the inverse scatteringcompensation processing. Control proceeds to step 126 where a secondtype of compensation processing is performed in connection withattenuation compensation. Processing steps 124 and 126 may be includedwithin compensation processing module 102 in an embodiment. Controlproceeds to step 128 where event identification processing may beperformed. In one technique that is described in paragraphs elsewhereherein, event identification processing is performed by utilizing thederivative of the TDR wave form. At step 130, classification processingis performed which in this embodiment is parametric classificationprocessing. An embodiment may utilize this or one or more other types ofclassification processing techniques to produces results in accordancewith the identified events. At step 132, the results are provided as anoutput of the classification processing, for example, to a user. Theparticular result output may vary in each embodiment. Different types ofresults are described elsewhere herein in more detail. Control proceedsto step 134 where a determination is made as to whether additionalsignals are to be processed. If there are no additional signals,processing stops. Otherwise, control proceeds to the top of the loop atstep 122 where the next subsequent signal is received and processed.

It should be noted that in connection with the foregoing processingsteps of flowchart 120, an embodiment may optionally omit one or more ofthe foregoing steps. Additionally, an embodiment may use one or morealternative techniques in place of, or in conjunction with, thosetechniques described herein. For example, an embodiment may use analternative technique to perform event identification processing such asmatched filters, wavelets, neural networks or a pattern recognitiontechnique different than as described elsewhere herein.

The inverse scattering problem, as may be applied for use with thesystem described herein for wire diagnostics, involves a one-dimensionalsystem of layered media in which current and voltage are the two statevariables that may be represented by two coupled first-order partialdifferential equations referred to herein as the Upward and DownwardEvolution equation (the Evolution equation) and the Discontinuityequation described in more detail elsewhere herein.

The Evolution equation is based on downward and upward moving waves inwhich the upward moving wave (U) represents the reflected voltage(Vrefl), and the downward moving wave (D) represents the incidentvoltage (Vinc) of the signal sent out, such as by the signal generator44. The measured voltage (Vmeas), such as at the pin connection 42 for awire, may be represented as:Vmeas=Vinc+Vrefl  EQUATION 1When the impedance Z is constant, the D and U waves do not interact anddo not change shape. When Z changes, D and U interact causing multiplereflections, such as in the presence of wire faults. D and U aredisturbed or change their shape where they cross a discontinuity as maybe represented by the Discontinuity Equation. This interaction between Dand U complicates transmission and reflection and it is this interactionthat is de-convolved in the inverse scattering problem.

The D and U waves travel without change of shape when the characteristicimpedance does not change and such behavior may be represented in thefollowing Evolution equation of matrices:

$\begin{matrix}{\begin{bmatrix}{D\left( {{{id} -},t} \right)} \\{U\left( {{{id} -},t} \right)}\end{bmatrix} = {\begin{bmatrix}d & 0 \\0 & d^{- 1}\end{bmatrix}\begin{bmatrix}{D\left\lbrack {{{\left( {i - 1} \right)d} +},t} \right\rbrack} \\{U\left\lbrack {{{\left( {i - 1} \right)d} +},t} \right\rbrack}\end{bmatrix}}} & {{EVOLUTION}\mspace{14mu}{EQUATION}}\end{matrix}$The D wave is just before a discontinuity at id (the ith delay operator)at any given time t and departed from (i−1)d at the instant t−d. Thewave has traveled without any change in shape such thatD(id−,t)=D[(i−1)d+,t−d)]  EQUATION 2The value of the right hand side of the above equations, D[(i−1)d+,t−d],at the instant prior to t−d is obtained from D[(i−1)d+,t] by executingthe delay operator d which changes any function of time f(t) into itsvalue at the instant t−d such that df(t)=f(t−d). EQUATION 2 above may berewritten as:D(id−,t)=dD[(i−1)d+,t)]  EQUATION 3Similarly, the equation for the U wave may be represented as:U [(i−1)d+,t]=U(id−,t−d)=dU(id−,t)which can be inverted to giveU(id−,t)=d ⁻¹ U[(i−1)d+,t)]  EQUATION 4The foregoing EQUATION 3 and EQUATION 4 may be combined to produce theEvolution Equation set forth above.

The following equation describes how the U and D waves interact as theypass through a discontinuity between Zi and Z_(i−1).

$\begin{matrix}{\begin{bmatrix}{D\left( {{{id} +},t} \right)} \\{U\left( {{{id} +},t} \right)}\end{bmatrix} = {H_{i}{H_{i - 1}^{- 1}\begin{bmatrix}{w\left( {{{id} -},t} \right)} \\{p\left( {{{id} -},t} \right)}\end{bmatrix}}}} & {{DISCONTINUITY}\mspace{14mu}{EQUATION}}\end{matrix}$where H is the evolution transfer function. In contrast to D and U, wand p are waves that changes their shape while traveling the medium andare unchanged as they cross a discontinuity at point id. The pressure, pof the downward moving wave D, is equal to the characteristic impedancemultiplied by the elastic velocity w, while the pressure of the upwardmoving wave U is the negative of this. When modeling transmission lines,pressure p is analogous to voltage and elastic velocity w is analogousto current. The notation id− represents a point in time just before thediscontinuity id and similarly the notation id+ represents a point intime just after the discontinuity id such that:D(id+,jd)=Di,j U(id+,jd)=Ui,jD(id−,jd)=D _(i−1 ,j−1) U(id−,jd)=U _(i−1 ,j−1)

The Evolution Equation and the Discontinuity Equation may be combinedinto a single matrix equation that represents the behavior of U and D:

$\begin{matrix}{\begin{bmatrix}{{D\; i},j} \\{{U\; i},j}\end{bmatrix} = {{\frac{1}{\sigma\; i}\begin{bmatrix}1 & {\;{{- \gamma}\; i}} \\{\gamma\; i} & 1\end{bmatrix}}\begin{bmatrix}{{{D\; i} - 1},{j - 1}} \\{{{U\; i} - 1},{j + 1}}\end{bmatrix}}} & {{COMBINED}\mspace{14mu}{EQUATION}}\end{matrix}$for a series of voltage measurements in accordance with the notationdescribed above.

Additionally, γi represents the current reflection coefficient at atime, i, which is the ratio of the reflected voltage, Vrefl, over theincident voltage, Vinc, at this time and may be represented as:γi=U _(i−1,i) /D _(i−1,i−1)

and σi represents the transmission coefficient at a time, i, which maybe represented as: √{square root over (1−(γi)²)}.

In embodiments using a wire or line that has a high level of processnoise or the Analog to digital converter has small number of bits (e.g.8 bits vs. 14 bit), the noise will introduce process errors into theinverse scattering algorithm. This error grows, potentiallyexponentially, with the length of wire under test. In this instance, anembodiment may include an error correcting strategy. In one errorcorrecting strategy, the reflection coefficient γ_(i) is set to zero ifthe absolute value of γ_(i) is less than a predetermined threshold thatmay vary in accordance with each embodiment. For a noisy system, forexample, a threshold of 3 times the standard deviation of the noise maybe used. For a low bit rate analog to digital converter, for example, athreshold of 0.5* Voltage/2^(number of bits) may be used. As an example,for a 0.5 volt pulse system, the threshold using the foregoing is:t=0.5/2⁷=0.002 _(γi.)

Below is a pseudo-code like description of one implementation of theforegoing Combined Equation. Note that this utilizes array notationwhich has index=1 as its first element.

Vrefl: Reflected Voltage; Vmes: Measured voltage; Vinc: Incident VoltageN = length (Vmes); % This is the number of sample points Vref = Vmes−Vin; Z(1) = Zo; % Initialize based on wire characteristic impedance ofnominal wire without faults For i = 1:N,    D(1,i) = vinc(i);%Initialize Upward and downward Wave matrices    U(1,i) = vrefl(i); endfor i = 1:N−1,  ii = i+1;  r(ii) = U(i,ii)/D(i,i); %Determine thereflective coefficient γi  if r(ii) > 1, %Avoid possible divide by zeroerrors   r(ii) = .999;  end  if r(ii) < −1,   r(ii) = −.999;  end  s(ii)= sqrt(1−r(ii){circumflex over ( )}2); %Determine transmissioncoefficient σi  for j = i:(N−1), %Inner loop --- adjust values in uppertriangular portion with respect to “i”   jj = j+1; %  THIS IS THECOMBINED EQUATION ABOVE   D(ii,jj) = (D(i,j) − r(ii)*U(i,jj))/s(ii);  U(ii,jj) = (−r(ii)*D(i,j) + U(i,jj))/s(ii);  end endUsing the foregoing values as estimated and included in the diagonals ofthe matrices U and D above, corrected voltages can be calculated fromthe relationship between characteristic impedance, voltage andreflection coefficient:Z1=Zo*(1+_(γ0)))/(1−_(γ0)))  EQUATION 5andVrefl(1)=(Z1−Zo)/(Z1+Zo)*Vinc(1)+Vinc(1)  EQUATION 6Below is the corresponding pseudocode-like representation which usesEQUATION 5 and EQUATION 6 to determine the adjusted impedances andreflected voltages:

for i = 1:N % Adjust to determine final values Z(i + 1) = Z(i) * (1 +r(i))/(1 − r(i)); Vrefl (i) = (Z(i + 1) − Zo)/(Zo + Z(i + 1)) *Vinc(i) + Vinc(i) end

In the foregoing, it should be noted that Zo is the known characteristicimpedance of the wire without any faults that may be determinedempirically and may vary in accordance with each embodiment. The outputof the foregoing is the corrected impedance Z and the correctedreflected voltage Vrefl for each point in time. Matrices D and U in thisembodiment may be characterized as triangular. At each point in time,“i”, the voltages in the upper triangular portion of the matrix arecorrected with respect to the current point in time being examined. Theforegoing Combined Equation incorporates a scattering matrixrepresenting the transmission and reflection of energy based on thecharacteristic impedance at that point. The left hand side of theCombined Equation represents corrected matrices of D and U voltagevalues up to a point in time. At a time “i”, a reflective voltage valueis measured and, based on this, additional entries in the matrices basedon subscript “j” (which ranges from “i” to the maximum dimension “n”)are corrected. In connection with the D and U matrices, for a value onthe diagonal of an entry x,x, the remaining values in the xth row of theD and U matrices are adjusted such that the entry x,y, y>x, for each y,is corrected. The voltage at a point “i” is adjusted based on thereflections from this point to the end of the wire.

Prior to executing the steps to adjust voltages to account for thereflections due to the inverse scattering problem, N reflective voltagesare measured. The foregoing embodiment uses an N×N matrix for D and U.The reflected voltages measured are an input to this technique and arestored as the 1^(st) row of the U matrix. Similarly, the N measuredincident voltages are an input and stored in the 1^(st) row of the Dmatrix. After the foregoing processing steps are executed, the diagonalsof the U and D matrices include the adjusted or corrected voltages withthe reflective components due to the inverse scattering problem removed.In connection with both the D and U matrices, the columns representforward (e.g. causal) time steps. The diagonals of each matrix, wherethe row and column indices are the same, represent the causal effect oftime, e.g. no voltage can be reflected at point i+1 until time aftertime i. For example, no reflected voltage can be measured for time index3 until time index 2 has happened.

Note that using the foregoing technique to remove the unwantedreflective components, voltage is measured where the voltage is afunction of true changes in impedance and artifacts from the multiplereflective components. As described elsewhere herein, the reflectioncoefficient is the ratio of Vrefl(i)/Vinc(i), and the measured voltageVmeas(i)=Vrefl(i)+Vinc(i). The foregoing technique uses the reflectioncoefficients because of the application of conservation of energyprinciples. The pseudo-code above uses “r” to indicate the amount ofenergy reflected, reflection coefficient, and the transmitted energy ist=sqrt(1−r^2 ), which is the transmission coefficient. The incidentvoltage (Vinc) after a transition at point “i” may be represented asVinc(i+1)=Vinc(i) t, while the reflected voltage is just Vinc(i)* r(i).At each point where there is a transition from one characteristicimpedance to another, the reflection coefficient isr(i+1)=(Z(i+1)−Z(i))/(Z(i+1)+Z(i)). Therefore if the true reflectioncoefficient is determined at each point, the adjusted or true Z at eachpoint may also be determined. Each of the D and U matrices are keepingtrack, respectively, of the incident and reflected voltages based on theupdated reflection coefficients determined using the measured voltage,inferred reflection coefficients and calculated transmitted voltage.

It should be noted that an embodiment may use other data structures andarrangements in implementing the foregoing techniques to compensate thereflected and incident voltages. For example, another embodiment mayutilize a single matrix to store the foregoing U and D matrices which isan N×1, N×1 matrix combining the two upper right triangular U and Dmatrices into a single matrix.

Referring now to FIG. 4, shown is a flowchart 140 of processing steps ofone embodiment for compensating or adjusting the incident and reflectivevoltages to account for the inverse scattering. The flowchart 140generally describes the steps set forth above and is one embodiment ofmore detailed processing of step 124 of FIG. 3. At step 142, the U and Dmatrices are initialized. The U matrix corresponds to the reflectedvoltage values measured which are known inputs, and the D matrixcorresponds to the incident or transmission voltage values which areknown inputs. As described above, these values may be placed in thefirst rows of the D and U matrices. At step 144, index variable i isinitialized to 1 and at step 146, the index variable ii is initializedto be the quantity i+1. At step 148, the reflective coefficient of ii isdetermined. At step 150, the transmission coefficient of ii isdetermined. At step 152, the index variable j is initialized to i and atstep 154, the index variable jj is initialized to be the quantity j+1.At step 156, the value of the D matrix at entry D(ii,jj) is adjusted andat step 158, the value of the matrix U at entry U(ii,jj) is adjusted. Atstep 160, a determination is made as to whether the value of j isgreater than the quantity N−1, where N is the number of sample points.If not, control proceeds to step 168 where j is incremented and controlproceeds to step 154 where the next iteration of the inner loop isperformed until the quantity of j at step 160 reaches the final value ofN. At step 160, when it is determined that j is greater than thequantity N−1, control proceeds to step 162 where a determination is madeas to whether the value if i is greater than the quantity N−1. If not,control proceeds to step 168 where the value of i is incremented.Control then proceeds to the top of the outer loop where the next outerloop iteration is performed. At step 162, if it is determined that thevalue of i is greater than the quantity N−1, then control proceeds tostep 164 where the adjusted reference voltages and impedance values aredetermined such that they are compensated in accordance with the inversescattering values determined.

Referring now to FIG. 5A, shown is a graphical illustration 180 of howthe foregoing reflective artifacts may appear in a measured waveform.The reflective artifacts, as indicated by the solid line 182, are thosereflections which are removed by the processing steps of FIG. 4. Thedashed line 184 represents the true impedance of the wire with thereflective artifacts or components removed. Without the reflectivecomponents caused by the scattering problem in a wire with no faults orevents, there would appear graphically a straight horizontal line with aconstant measured impedance. However, with the reflection components dueto a fault in the wire and/or the scattering problem, measurements atdifferent points in time result in a waveform as shown in 180 in whichthe varying reflective artifacts cause an additional unwanted change inthe waveform of the measured impedance. In a wire with faults, there maybe changes in the impedance indicated by changes in the waveform.However, the unwanted reflective components or artifacts due to thescattering problem cause extra “noise” in this waveform. Accordingly,the waveform 180 needs to be adjusted to compensate for those unwantedreflective components due to the scattering problem.

Referring now to FIG. 5B, shown is another illustration 185 comparing ameasured waveform to a waveform that has been adjusted to remove thereflective components due to the inverse scattering problem. Themeasured waveform 186 includes voltage changes due connectors as well asreflective components. The adjusted waveform 188 includes those incidentand reflective components due to the connectors in this example, but hasbeen adjusted to remove the reflective components. It should be notedthat other examples would include other peaks due to other events, suchas a damaged or crimped wire, in place of the peak in the waveformassociated with the connector. The particular waveform varies inaccordance with the wire and any defects, connectors, and the likeassociated with each wire.

Referring now to FIG. 6, shown is a graphical illustration 190 of theinverse scattering problem and the associated reflective artifacts. Thesolid arrows 192 a-192 d indicate the adjusted or inferred measuredwaveform Z at a particular point in time determined in accordance withcorrected or adjusted reflective and incident voltage values. Theadjusted reflected voltage values at different points in time are storedin the diagonals of the U matrix. The adjusted incident voltage valuesat different points in time are stored in the diagonals of the D matrix.

The one or more reflective components as associated with the previouslydescribed U matrix are the dashed arrows sloping down to the right 194a-194 l. The one or more incident components as associated with thepreviously described D matrix are the dashed arrows sloping upward tothe right 193 a-193 j. After executing the processing steps describedherein, the original measured incident and reflective voltage values areadjusted to remove reflective components caused by the reflectivescattering problem.

Measured voltages are indicated as 195 a-195 e. It should be noted thatthe foregoing incident and reflective components each include twoportions: a first portion representing an adjusted portion and a secondportion representing the contribution due to the inverse scatteringproblem.

In one embodiment, after the reflective voltages and associatedimpedances are adjusted to take into account the inverse scatteringproblem, these adjusted values may be used as inputs to attenuationcompensation processing as set forth, for example in step 126 of FIG. 3.

In one embodiment, the output of inverse scattering compensationprocessing, which is used as an input to attenuation processing, is asingle vector of voltages, denoted VADJ[1 . . . N], where “N” is thenumber of measured voltages as referenced above. Each of the VADJ[i],i=1 . . . N, are the previously measured voltages which have beenadjusted to remove the reflective artifacts, such as using theprocessing steps described in connection with FIG. 4. EachVADJ[i]=Vrefl,adj[i]+Vinc,adj[i]where

Vrefl,adj[i] is the adjusted reflective voltage at time “i” and

Vinc,adj[i] is the adjusted incident voltage at time “i”.

This relationship is based on:Vmeas [i]=Vrefl [i]+Vinc [i]where:

Vmeas[i] is the measured voltage, Vinc[i] is the known incident voltagesent out on the wire at time “i”, and Vinc[i] is inferred by subtractingVinc[i] from the quantity Vmeas[i].

Each Vrefl,adj[i] may be determined using

for i = 1:N % Adjust to determine final values Z(i + 1) = Z(i) * (1 +r(i)); Vrefl (i) = (Z(i + 1) − Zo)/(Zo + Z(i + 1)) * Vinc(i) + Vinc(i)end

as set forth and described elsewhere herein. Each Vinc,adj[i] may bedetermined as D[i,i], i=1,N, from the diagonal of the D matrix afterperforming FIG. 4 processing steps as described elsewhere herein.

As the voltage waveform travels down the wire, it is subject to afrequency-dependent attenuation where higher frequency components of thewaveform are attenuated to a greater degree than lower frequencycomponents of the waveform. In addition, the amount of attenuation atall the frequencies depends on the distance traveled by the waveform.Thus, a signal reflected from an anomaly at one meter would lookdifferent than a signal from a reflection of an anomaly at one hundredmeters, even if both anomalies are identical. Accordingly, it isdesirable to compensate for the frequency and length dependentattenuation so that an anomaly will cause the same reflective signal tobe sensed irrespective of the distance of the anomaly to the point wherethe signal is measured. In an embodiment herein, the VADJ[1] throughVADJ[N] voltage waveform signal generated by the process described aboveis further compensated to provide a compensated voltage waveform signal,VC[1] through VC[N], which represents the VADJ[1] through VADJ[N] signalcompensated for frequency and length dependent attenuation.

An equation that describes attenuation of a voltage signal as a functionof frequency and length of travel of the signal is the following:A(f, L)=e ^(−(R (f)*L/Z0))

Where Z0 is the characteristic impedance of the cable and R(f) is thefrequency dependent resistance of the cable. The frequency dependentresistance, R(f), may be determined using the equation:R(f)=(½r)* (μf/πσ)^(1/2).

Where r is the radius of the wire, μ is the permeability of free space,in henries per meter, and σ is the conductivity of the conductormaterial of the cable. For copper conductors, σ is approximately 5.8×10⁷ohms/meter.

Note that the quantities r and σ are constant for a given cable (as, ofcourse are μ and π). Thus, R(f)=K * f^(1/2). More information aboutdetermining cable attenuation and the relationship thereof to frequency,length, and impedance, may be found in Heald, Mark A. and Marion, JerryB., Classical Electromagnetic Radiation. Fort Worth, Harcourt BraceCollege Publishers, 1995 and in Hall, Stephen., Hall, Garret., McCall,James., High Speed Digital System Design. New York, John Wiley & Sons,Inc., 2000.

Although attenuation is a function of both frequency and length, in anembodiment herein the attenuation is approximated by assuming that thelength is a constant equal to the round trip length of the cable (i.e.,twice the cable length). In the case of such an assumption, theattenuation becomes a function of just the frequency rather than bothfrequency and length. As discussed in more detail below, in oneembodiment, the length is set to the round trip length of the cable andonly the frequency is taken into account when determining theattenuation and appropriate compensation. In another embodiment, boththe frequency and length are used to determine and compensate for theattenuation.

Once the attenuation is determined, it is desirable to provide a gainfilter that is the inverse of the attenuation so that the convolution ofthe attenuation and gain functions (in the time domain) or themultiplication of the attenuation and gain functions (in the frequencydomain) cause the resulting signal to be unattenuated. That is, the gainfilter is applied to the attenuated signal to remove the affects ofattenuation therefrom.

Given that the attenuation may be determined as set forth above, it isfairly straight forward to calculate the gain required to offset theattenuation and then to design an FIR (finite impulse response) digitalfilter to provide that gain. Such a procedure is described, for example,in Oppenheim, Alan V., Schafer, Ronald W., Discrete-Time SignalProcessing. New Jersey, Prentice Hall, 1989 and McClellan, James, et al.Computer-Based Exercises for Signal Processing Using Matlab 5. NewJersey, Prentice Hall, 1998. Of course, the number of coefficients forthe FIR filter is a design choice. A greater number of coefficientsincreases the precision of the result while a lesser number ofcoefficients decreases the computational time required for the filter.

Referring to FIG. 7, a flowchart 230 illustrates steps performed inconnection with compensating a voltage signal to account forattenuation. The input signal, VADJ[1] through VADJ[N], is representedby a series of voltages each measured at a particular point in time, andthus indexed by one through N where N is the maximum number of samples.The object of attenuation compensation is to convert each of the pointsVADJ[1] through VADJ[N] into compensated voltage signals VC[1] throughVC[N]. Note that, in theory, VC[1] is a function of each and everyVADJ[1] through VADJ[N] value, VC[2] is a function of each and everyVADJ[2] through VADJ[N], VC[3] is a function of each and every VADJ[3]through VADJ[N], etc. Thus, it would be possible to use an FIR filterwith N coefficients to perform the compensation. However, practicallyspeaking, it is often sufficient to provide a filter with lesscoefficients. In one embodiment, fifty filter coefficients may be usedwhile in another embodiments only five filter coefficients may be used.Of course, other numbers of filter coefficients (between five and fiftyor greater than fifty or less than five) may also be used.

Processing for the flowchart 230 begins at a step 232 where indexvariable, i, is set equal to one. The index variable i is used to indexthrough each of the VADJ values and each of the VC values. Following thestep 232 is a step 234 where the characteristic impedance of the cable,Z₀, is determined. The characteristic impedance, Z₀, may be providedusing any one of a number of techniques. For example, Z₀ may be input bya user who obtains the value from a manual (or other source) for theparticular type of cable being tested. Alternatively, Z₀ may bedetermined from the measurements of the cable using techniques describedbelow.

Following the step 234 is a step 236 where the value of L is determined.In an embodiment herein, the value of L determined at the step 236equals the length of the cable times 2 (i.e., the roundtrip length forthe signal). Determining the length of the cable is described in moredetail below. In other embodiments, L is allowed to change as a functionof i. Note that the length traveled by a particular portion of thesignal VADJ[i] is a function of the time it takes for the signal to makea roundtrip. In any event, for an embodiment illustrated herein, thevalue of L used at the step 236 corresponds to twice the length of thecable being tested, which is determined using techniques describedbelow. However, note that, just as with Z0, it is possible to have auser enter the value of L as an input.

Following the step 236 is a step 238 where the attenuation is determinedgiven the value of Z0 calculated at the step 234 and the value of Ldetermined at the step 236. For an embodiment described herein, both Z0and L do not change so that the attenuation is constant and isdetermined one time at the step 238. However, for alternativeembodiments (described below), L varies for each point VADJ[i] so that anew attenuation will be calculated for each new L at the step 238.

Following step 238 is a step 242 where filter coefficients g[0] throughg[K−1] are calculated based on the attenuation determined at the step238. The number of filter coefficients is represented by K. As discussedabove, it is straight forward to determine the filter coefficients foran FIR filter given the characteristic attenuation (and thus desiredgain) for a cable. In addition, the value of K, the number of filtercoefficients, is a design choice, as discussed elsewhere herein.

Following the step 242 is a step 244 where the value of VC[i] is set tozero. As discussed elsewhere herein, the end result of performing thesteps of the flowchart 230 is an array of compensated voltages VC[1]through VC[N], where N is the number of measured points of the voltagewaveform.

Following the step 244 is a step 246 where an index variable, j, is setequal to zero. The index variable j is used to index through the filtercoefficients, as described in more detail below. Following step 246 is astep 248 where the value of VC[i] is set equal to the sum of VC[i] plusthe value of VADJ[i+j]* g[j].

Following the step 248 is a step 252 where the index variable, j, isincremented. Following the step 252 is a step 254 where it is determinedif the index variable, j, is less than K, the total number of filtercoefficients. If so, then control transfer from the step 254 back to thestep 248 to continue calculating VC[i]. Thus, the value of VC[i] iscalculated using the loop comprising the steps 248, 252, 254 to providethe FIR filter functionality.

Once it is determined at the step 254 that the value of the indexvariable j is not less than the value of K, the number of filtercoefficients, control transfers from the step 254 to a step 256 wherethe index variable i, which is used to index VADJ and VC, isincremented. Following the step 256 is a test step 258 which determinesif i is less than N, the total number of points being processed. If not,then processing is complete. Otherwise, control transfers from the step258 back to the step 244 to calculate the next VC[i].

In an alternative embodiment, the length is allowed to be a function ofthe index variable i, where L is proportional to i since each irepresents a different point in time. Thus, for each new value for L, anew value for the attenuation is determined and a new set of filtercoefficients is also determined. Although this alternative embodimentmay be more computationally intensive than the embodiment describedabove, it has the advantage of using a different filter at each lengthto account for the fact that attenuation (and thus the desired gain) isa function of both the frequency of the signal and the length that thesignal has traveled.

The alternative embodiment is illustrated by an alternative path 262from the step 258. If it is determined at the step 258 that the indexvariable i is less than N, the total number of VADJ and VC points, thencontrol transfers from the step 258 along the alternative path 262 backto the step 236 to determine L where, for this alternative embodiment, Lis a function of the index variable i. The new value of L calculated atthe step 236 based on the value of i may then be used at the followingstep 238 to recalculate the attenuation. The new value for theattenuation calculated for step 238 may be then used to calculate a newset of filter coefficients at the step 242. Thus, for this alternativeembodiment, new filter coefficients are calculated at the step 242 foreach VADJ[i]. Following the step 242 is the step 244 and follow onsteps, described above, which proceed as set forth above in connectionwith the previous embodiment.

Referring to FIG. 8, a flowchart 280 illustrates steps for determiningthe length and characteristic impedance of a cable, which are used inthe processing described above in connection with the flowchart 230 ofFIG. 7. Processing begins at a first step 282 where the maximum andminimum voltage values, VMAX and VMIN, are determined in a straightforward manner by examining all of the VADJ[1] through VADJ[N].Following the step 282 is a step 284 where the first derivative of theVADJ signal is determined in a conventional fashion by, for example,subtracting VADJ[i+1] from each VADJ[i] for all i's one through N−1.

Following the step 284 is a test step 286, where it is determined if theend of the cable is terminated by an open circuit or a short circuit (orcomponents that approximate open or short circuits). In an embodimentherein, the first value of VADJ (VADJ[i]) is used. Note that VADJ[1]represents the voltage value at the test harness. In an embodimentherein, if (VMAX−VADJ[1]) is greater than (VADJ[1]−VMIN), then it isassumed that the cable is terminated by an open circuit (or equivalent).Otherwise, it is assumed that the cable is terminated by a short circuit(or equivalent).

If it is determined at the test step 286 that the cable is notterminated by an open circuit, then control passes from the step 286 toa step 288 where the index, NEND, of the minimum value for the voltageof the derivative (determined at the step 284) is determined. Otherwise,if it is determined at the test step 286 that the cable is terminated byan open circuit, then control passes from the step 286 to a step 292,where the index, NEND, for the maximum value for the voltage of thederivative (determined at the step 284) is determined.

Following either the step 288 or the step 292 is a step 294 where thecable length is calculated in a straight forward manner using the index,NEND, determined at the step 288 or the step 292. Since the indexrepresents time, then the length of the cable is calculated bymultiplying the speed of the waveform by the time represented by theindex. Following the step 294 is a step 296 where VMED, the median valueof the voltages between and including VADJ[1] and VADJ[NEND] isdetermined in a straight forward manner. Following the step 296 is astep 298 where the impedance is calculated using the formula Z0 equals(fifty*VMED)/(VIN−VMED), where VIN is the magnitude of the incidentinput voltage provided by the signal generator 44 shown in the diagram40 of FIG. 1.

Once the signal compensation processing has been performed to equalizefor attenuation or dispersion loss and remove multiple inversescattering reflections, events of interest are detected in preparationfor parametric classification. An event of interest is any change incharacteristic impedance in a wire, including a connector element, cut,nick, crimp, insulation damage, or coupling with other structures orwires.

An event, once identified, is passed to the classification component toclassify the type of event; however, one issue is to balance theprobability of an event detection with the probability of a false alarm.Generally, an effective event detection system will have as low aprobability of false alarm as possible while still maintaining anacceptable probability of detection of an event of interest. Efficientprocessing and classification of a signal is accomplished by classifyingonly events for which there is a certain probability that an event ofinterest has been identified. Such operation reduces wasted processingtime in sending false alarms to be classified by the parametricclassification operations.

False alarms usually occur because of system noise. Every systemgenerally has system noise which is typically of a Gaussiandistribution. Noise occurs due to electromagnetic interference as wellas sampling noise resulting from an Analog to Digital conversion process(for example, the A/D converter might only have ten bits, giving rise toone thousand and twenty four distinct measured voltages). Other problemsthat affect successful event detection include the fact that the wireitself is not perfectly lossless, meaning that the characteristicimpedance rises slightly with length. Thus, simply assigning voltagethresholds does not adequately distinguish between wire properties (suchas low or high characteristic impedance) or noise signals and trueevents, such as a cut, crimp, or other fault.

Referring now to FIG. 9A, a flowchart 300 is shown having steps foridentifying events with a controlled false alarm rate according to oneembodiment of the invention. For the system described herein, events aredefined as portions of the signal where the first derivative exceeds apredetermined threshold. In some embodiments, an additional criteria maybe imposed where, in addition to the derivative exceeding apredetermined threshold at a particular point, there is also a rateincrease for the signal so that VC[k+1]/VC[k] is greater than a secondpredetermined threshold for two, three, or some other number ofsuccessive points starting at the particular point.

At a step 302, the signal VC[1] through VC[N] is received having awaveform that has been compensated for attenuation and dispersion lossand corrected to remove multiple inverse scattering reflections.Following the step 302 is a step 304, where the first derivative (dv/dt)of the signal is taken. This step is accomplished by taking the timedifference of the voltage waveform:dv[i]=VC[i−1]−VC[i], for i=2 to N.By taking the derivative, the effects of wire loss and changes incharacteristic impedance due to coupling are substantially removed sincethese events are often characterized by small changes in voltage versustime, causing the first derivative to be approximately zero. Further,examining and analyzing the raw VC[1] through VC[N] signal waveform todetermine an event of interest with no initial information is notnecessarily effective because mean voltage of the signal is not known,thereby preventing the establishment of a voltage threshold. Examinationof the first derivative of the waveform removes this issue because thefirst derivative of the mean voltage is zero.

Unlike wire loss and characteristic impedance, the effect of systemnoise is not necessarily eliminated by taking the first derivative.Accordingly, following the step 304 is a step 306, where a standarddeviation of the first derivative of the noise is calculated orestimated. Like the system noise, the first derivative of the systemnoise is typically Gaussian. Accordingly, at the step 308, an eventdetection threshold is set such that when the absolute value of thewaveform derivative exceeds the threshold, an event is detected. Thefirst derivative of the impedance changes due to connectors, opens,shorts or faults is relatively large compared to the system noise andare therefore detectable and distinguishable. Events below the thresholdcan be not distinguished without increasing the false alarm rate, and ingeneral, are often not significant events.

In an embodiment described herein, the event detection threshold may beestablished by calculating (or estimating) the standard deviation of thewaveform derivative on a portion of the waveform signal free fromdefects. For example, the wire under test may be connected to the testset via a test harness. The test harness is a nominal fifty Ohm coaxialcable with known length, which is ideally suited for generatingthreshold statistics. The threshold statistics are set based on thestandard deviation measure. For example, in a preferred embodiment, thethreshold is set at three times the standard deviation of the systemnoise test harness waveform derivative which may provide a false alarmrate of two in one thousand events (0.002).

Following the step 308 is a step 310, where a differential voltage peakis identified in which the absolute value of the peak exceeds the setevent detection threshold. Such a peak indicates a high probability ofan event of interest. Following the step 310 is a step 312, where theportion of the signal VC[1] through VC[N] that corresponds to theidentified differential voltage peak is identified. Following the step312 is a step 314, where the signal portion identified at the step 312is stored temporarily in preparation for being sent to be classified, asfurther described elsewhere herein. Following the step 314 is a step316, where it is determined whether other peaks that exceed theestablished event detection threshold exist. If so, then controltransfers from the step 316 to the step 310, described above. Otherwise,control transfers from the step 316 to a test step 318, where it isdetermined whether a new threshold is to be established. In someembodiments, multiple thresholds may be used where each is establishedby a different criteria. In addition, it is possible to decide to use anew threshold established using different criteria based on the numberof events detected (e.g., for a low number of events, lower thethreshold and for a high number of events, raise the threshold). In someembodiments, the events stored at the step 314 may be discarded if a newthreshold is established. Alternatively, it is possible to simply addnew events to the events already stored. If it is determined at the step318 that a new threshold is to be established, control transfers fromthe step 318 back to the step 308, discussed above. Otherwise, controltransfers to the step 322, where the events stored at the step 314 areclassified, as described in more detail below. Following the step 322,processing is complete.

It may be desirable in an embodiment to use a different technique otherthan the processing steps described in connection with the flowchart ofFIG. 9A. There are instances in which the foregoing described inconnection with FIG. 9A may tend to amplify any noise such as, forexample, the effect of environmental noise and noise in connection withanalog to digital conversion. As an alternative, an embodiment may uselow pass filtering to remove such noise. However, certain types offilters, such as FIR filters, may actually remove or filter out data ofinterest. For example, use of an FIR filter in connection with theprocessing steps of FIG. 9A maintains the first moment or the meanvalue, but actually modifies the second moment which is not desirable inconnection with event detection.

Accordingly, what will now be described is another processing techniquethat may be used in connection with detecting an event on a wire undertest. The processing steps that will now be described “smooth out”, suchas by curve fitting, noisy data while maintaining the underlying shapeof the higher moments of the data. The technique described in followingparagraphs uses a polynomial to fit a portion of the compensated voltagedata points defined in accordance with a window size and a designateddata point. This provides for localized curve fitting for a predefinednumber of points before and after the designated point. The derivativeof each of these polynomials may now be taken. The Ith first derivativemay be evaluated at the Ith data point. Event detection may then beperformed using the evaluated first derivatives.

Referring now to FIG. 9B, shown is a flowchart 325 of processing stepsthat may be performed in another embodiment in connection with eventdetection. At step 326, a signal is received with a compensated andcorrected wave form. The input received at step 326 is similar to thatas described in connection with step 302 of FIG. 9A. At step 327, acurrent point is assigned to be the first voltage data point and thevariable I, which is used in following processing steps as a counter, isalso initialized to one (1). At step 328, a number of predefined orpredetermined points, denoted as N, are determined existing prior to thecurrent point. At step 329, a number of points, denoted as M, occurringafter the current point are also determined. As used herein, the numberof N points before the current point and the number of M points afterthe current point define a window of length N+M+1 points. Controlproceeds to step 330 where the Ith polynomial is determined inaccordance with the data centered at the current point using thepredetermined window of N+M+1 points. Any one of a variety of differentcurve fitting techniques may be used to determine the Ith polynomial inaccordance with the N+M+1 data points. A particular example is describedin more detail elsewhere herein.

Control proceeds to step 331 where the loop control variable I isincremented by 1, and the current point is designated as the next datapoint. At step 332, a determination is made as to whether processing iscomplete for all of the data points. If not, control proceeds to steps328 and 329 where a subsequent window is determined for the next datapoint and a polynomial is determined to fit that current data point andassociated window of data points. It should be noted that an embodimentmay use the same window size and values for M and N on each iteration.In this instance, values for M and N may be determined outside of theloop iteration prior to performing the first iteration.

At step 332, when all data points have been processed, control proceedsto step 333 where the variable I is re-initialized to one. At step 334,the first derivative of polynomial I, denoted as first derivative(I), isdetermined. It should be noted that the first derivative may bemechanically determined in accordance with well-known mathematicalrules. For example, in one embodiment, the first derivative may bedetermined using, for example, well-known algebraic differentiationrules. At step 335, the loop control variable I is incremented by one(1). A determination is made at step 336 as to whether all polynomialshave been processed. If not, control proceeds to step 334 where thefirst derivative of the next polynomial is determined. This processingproceeds until, at step 336, a determination is made that all firstderivatives have been determined. Control then proceeds to step 337where the first derivatives are evaluated at each voltage data point inaccordance with the associated window of data points. The events ofinterest for each of the first derivatives are then determined.

Referring now to FIG. 9C, shown is a flowchart of processing steps ofone embodiment for evaluating first derivatives at voltage data pointsand determining events of interest previously described in connectionwith FIG. 9B. Flowchart 337 of FIG. 9C shows more detailed processingsteps of one embodiment for step 337 referenced in FIG. 9B. At step 337a, variable I is initialized to one(1) and the variable current point isinitialized as the first voltage data point. The voltage data pointsused in flowchart 337 are the compensated voltages input at step 326. Atstep 337 b, the Ith first derivative, denoted as first derivative(I) inthe flowchart, is evaluated at the current point. Control proceeds tostep 340 where the variable I is incremented by one(1) and current pointis assigned to be the next voltage data point. At step 341, adetermination is made as to whether all the first derivatives have beenprocessed. If not, control proceeds to step 337 b to evaluate the nextfirst derivative. Otherwise, if all first derivatives have beenevaluated, control proceeds to step 342 where an event detectionthreshold is determined. Any one or more of a variety of differenttechniques may be used in connection the determining such a threshold,such as those described elsewhere herein in connection with FIG. 9A. Atstep 343, a determination is made as to whether there is a peak in theevaluated first derivatives exceeding the threshold. If not, controlproceeds to step 346. If so, control proceeds to step 344 where theevent signal portion corresponding to the first derivative peak isdetermined. An embodiment may use any one or more of a variety ofdifferent peak finding techniques, such as described in connection withFIG. 9A elsewhere herein. At step 345, the event determined may berecorded for further processing. At step 346, a determination is made asto whether an additional threshold is to be established. For example, ifno events are detected when using a first threshold, an embodiment maysubsequently, try a second different threshold. If additional thresholdsare to be established, control proceeds to step 342. Otherwise,processing in connection with flowchart 337 ends.

It should be noted that the processing steps of FIGS. 9B and 9C providean alternate technique in connection with determining first derivativevalues. These first derivative values are used rather than thecompensated voltages when performing event detection. An embodiment mayuse one or both of the foregoing first derivative techniques whenperforming event detection.

An embodiment may select various values for N and M as used in theforegoing. In one embodiment, N and M may be selected as the same sizesuch that there is no biasing in connection with N and M. N+M+1 form thewindow size which may vary in a particular embodiment. The window sizeselected in an embodiment may be inversely related to the bandwidth of asystem. For example, a larger window size may be used in a system havingless bandwidth, and a smaller window size may be selected in systemswith larger bandwidths.

It should be noted that any one of a variety of curve fitting techniquesmay be used in an embodiment in connection with step 330 processing.Recall, step 330 processing may include determining a polynomial using acurve fitting technique in accordance with each particular window ofdata points with respect to a current data point. In one embodiment, theleast-squares curve fitting technique may be used and the normalequations may be used in solving for the coefficients of thepolynomials. Techniques such as this and others that may be used arewell-known as described, for example in, Numerical Recipes in C, Pres,William, Teukolsky, Saul, Vetterling, Willian and Flannery, Brian,Cambridge University Press, Cambridge, 1988. Generally, the polynomialsused in the foregoing processing steps of FIGS. 9B and 9C may berepresented as follows:a ₀ +a ₁ i+ . . . +a _(n) x ^(n)Normal equations for the above polynomial may then be represented as:A c=v  NORMAL EQTN 1where, as used herein:

A is matrix having N+M+1 rows (the size of the window) and n+1 columns;

c is a vector of coefficients; and

v is a vector of N+M+1 voltages.

Now, multiply both sides by A^(t), the transpose of matrix A, to get:A ^(t) v=A ^(t) A cand now solve for c, the coefficients to get:c=(A ^(t) A)⁻¹ A ^(t) v  COEFFICIENT EQTN

The normal equations may be used to solve for the coefficients ofpolynomial (I) using the associated window of data points associatedwith the Ith current data point.

Following is a pseudo code-like representation using the aboveCOEFFICIENT EQTN that may be used in determining the coefficients. Inthe following, each Ai,j=i^(j), i=−N, . . . M, and j=0, . . . ,n forvoltages V_(−N), . . . Vo, . . . , V_(M) where Vo is referenced as thekernel of v below and corresponds to the current voltage data point asused in connection with FIGS. 9B and 9C. Note that c₁ is the smoothedvalue of v, and c₂ is the first derivative values of v. In the followingdescription, c is an m×1 vector, where c(1)=is v smoothed, c(2) is thefirst derivative, c(n) is the n−1 derivative.

function vs = smth(v,m,d)  %smoothing function,  %v is an array ofvoltage  %m is the polynomial size (2, 3, 4 or higher)  %d is thederivative, 1 is zeroth, 2 is 1^(st) When d=1, just return smoothed    out original values in accordance with polynomial determined.  nr =8; %number of points prior kernel of v ;  Window size = nr+nl+1 which is17       ; in this example  nl = 8; %number of points after kernel of v idx = −nl:nr;  j = 0:m;  i = 1:length(idx);  for i = 1:length(idx),%build up A where Ai,j = i^(j) as indicated above.   A(i,:) =idx(i).{circumflex over ( )}j;  end    At = A′; This is a transposeoperator that determines the transpose of the parameter  AI = inv(A′*A);inv is a function that determines inverse of parameter  L = length(v); for i = nl+1:(L−nr);   crtI = idx+i;   f = v(crtI);   cn = AI*At*f;;Above COEFFICIENT EQUATION   vs(i) = c(d);  end  if d == 1, ; fill inbeginning and ending values for window size   vs(1:nl) = v(1:nl); ;depending on what derivative is being determined as ;indicated by “d”  vs((L−nr+1):L) = v((L−nr+1):L);  elseif d == 2,   vs(1:nl) = 0;  vs((L−nr+1):L−1) = 0;  elseif d == 3, ;This indicates the secondderivative   vs(1:nl) = 0;   vs((L−nr+1:L−2)) = 0;  end  vs = vs(:);;Returns array of smoothed voltage values for the polynomial when d=1; ;Returns array of first derivative values corresponding to voltage valueswhen d=2.

Referring to FIG. 10, a flowchart 350 illustrates in more detail theprocessing performed at the step 322 of the flowchart 300 of FIG. 9A andstep 338 of FIG. 9B where each of the events are classified. An event isidentified as a finite number of points VC[i] through VC[j] proximate tothe event detected at the step 310 of the where, for an embodimentherein, VC[i] (the first point of the event) is greater than thethreshold used at the step 310 and VC[i−1] is less than the threshold.For convenience, the points of each event will be referred to usingindex values one through M.

Processing begins at a first step 352 where the voltage values of theevent are converted to reflection coefficient values, denoted herein asRC[1] through RC[M]. A reflection coefficient is simply a scaling of thevoltage so that, irrespective of the magnitude of the input voltage, theanalyzed signal is the same. In an embodiment herein, voltages areconverted to reflection coefficients by dividing the voltage values bythe magnitude of the input voltage. Accordingly, assume that the inputvoltage is VINPUT, then the reflection coefficients, RC[1] through RC[M]are calculated by the formula RC[k]=VC[k]/VINPUT for k=1 through M.

Following the step 352 is a step 354 where an index, i, is set to zero.The index i is used to iterate through the events detected at the step310 and stored at the step 314 of FIG. 9A. Following the step 354 is atest step 356 which determines if the index variable, i, is greater thanthe number of events detected at the step 310 of FIG. 8. If i is greaterthan the number of detected events, then processing is complete.Otherwise, control passes from the test step 356 to a step 358 whereanother index variable, j, is set to zero. The index variable j may beused to iterate through different fault types stored in a library offault types. The library of fault types may be stored in the datastorage element 52 of FIG. 1 and contain different patterns, each ofwhich corresponds to a particular fault type. The patterns in thelibrary may contain wave form shapes corresponding to wire insulationbeing cut, the wire being crimped, etc.

Following the step 358 is a test step 362 which determines if the index,j, is greater than the number of fault types stored in the library. Ifnot, then control passes from the step 362 to a step 364 where a scoreis calculated for the event being analyzed (RC[1] through RC[M]) and thefault type j. For each event, there is calculated a number of scorescorresponding to the number of fault types. Calculating the score at thestep 364 is discussed in more detail hereinafter. Following step 364 isa step 366 where the index variable, j, is incremented to iteratethrough different fault types. Following the step 366, control transfersback to the step 362, discussed above.

If it is determined at the step 362 that the index variable j, isgreater than the number of fault types, then control passes from thestep 362 to a step 368 to select the highest score for event i amongeach of the scores calculated at the step 364. Following step 368 is atest step 372 which determines if the highest score for the event isgreater than a predetermined value (PDV). In an embodiment herein, thepredetermined value used at the test step 372 is zero. However, forother embodiments, the predetermined value may be different. Thepredetermined value used at the step 372 depends, in part, on theformula used to calculate the score at the step 364.

If it is determined at the test step 372 that the highest scorecalculated at the step 364 does not exceed the predetermined value, thencontrol transfers from the test step 372 to a step 374 where the event iis deemed not to correspond to any fault (i.e., corresponds to noise).That is, if no fault types correlate well with the event (i.e., no faulttypes generate a high enough score at the step 364), then it isdetermined that the event does not correspond to any fault type and thatthere is no fault.

On the other hand, if it determined at the test step 372 that thehighest scoring event is greater than the predetermined value, thencontrol transfers from the step 372 to a step 376 where the event isdeemed to correspond to a fault having the fault type that caused thehighest score. Thus, for example, if fault type number five (i.e. j=5)corresponded to the highest score calculated at the step 364, then thefault for the event set at the step 376 corresponds to fault type numberfive. Following step 376 and following step 374 is a step 378 where theindex variable, i, is incremented to iterate through the differentevents calculated at the step 310 of FIG. 8. Following step 378 controltransfers back to the step 356 discussed above.

Referring to FIG. 11, a flowchart 400 illustrates in more detailcalculation of the score for each of the faults in the fault library.Processing begins at the first step 402 where score [j] is initialized.As discussed above, the index variable j is used to iterate through thedifferent types of faults for each event. Thus, score[j] corresponds tothe score of the jth fault in the fault library for the event beingexamined RC[1] through RC[M]. In an embodiment herein, score[j] isinitialized to zero at the step 402. However, for other embodiments, itmay be possible to initialize score[j] to some other value.

Following the step 402 is a step 404 where an index variable, k, is setequal to one. The index variable k is used to iterate through each ofthe points of the event RC[1] through RC[M]. Following the step 404 is atest step 406 which determines if the index variable, k, is greater thanM, the number of points for the event. If so, then processing iscomplete. Otherwise, control transfers from the step 406 to a step 408to calculate the score.

In an embodiment herein, the score is calculated based on the valuesmeasured for the event RC[1] through RC[M], the expected values forrandom (non-fault) noise, the expected values for each fault in thefault library, and the expected variance of the fault pattern values. Asdiscussed above, the fault library contains patterns of different typesof faults. In the flowchart 400 of FIG. 11, the fault library isreferred to as FLIB[j, k], where the j index is the particular fault inthe fault library for which score [j] is being calculated and k is anindex to each of the points in the pattern in the fault library FLIB[j,k] that is compared to each point in the event RC[k].

In addition, in one embodiment, there is a stored array, NOISE[k], whichcorresponds to expected values for a pattern made by random (non-fault)noise. Note that if the event RC[1] through RC[M] corresponds toNOISE[k], then the calculated value of score[j] is expected to berelatively low. There is also an array VARIANCE[k] which indicates thevariance of the pattern stored in FLIB[j, k]. Note that a low variancewould tend to require the event RC[1] through RC[M] to match the patternstored in FLIB relatively closely to generate a particular score[j]whereas the same score[j] may be generated by a match between the eventRC[1] through RC[M] that is less close if there is a larger variance. Inother words, the lower the variance, the more closely an event has tomatch a particular pattern to generate a particular score.

At the step 408, score[j] is calculated by adding to the previouslycalculated score[j] using the following formula:score[j]=score[j]+(FLIB[j, k]−NOISE[k])*VARIANCE[k]*RC[k]+(½)*(NOISE[k] ² −FLIB[j, k] ²)*VARIANCE[k]

Following step 408 is a step 412 where the index variable, k, isincremented to iterate through each of the point of the event RC[1]through RC[M]. Following the step 412, control transfers back to thestep 406, discussed above, to determine if the index variable, k,exceeds the value M, the number of points in the event.

In some embodiments, it is possible to take into account the covarianceof each of the patterns stored in the fault library. The covariancerepresents that correlation between each point of the fault libraryFLIB[j, k1] and each other point FLIB[j, k2], where k1, k2 equal onethrough M. The covariance may be represented by a two dimensional squarematrix, COVJ, for each of the faults in the fault library where eachentry COVJ[k1, k2] represents the covariance between FLIB[j, k1] andFLIB[j, k2]. Note that when k1 equals k2, the value of COVJ[k1, k2]equals the variance VARIANCE[k1 or k2]. Note also that there may be acovariance matrix for the noise COVN.

Referring to FIG. 12, a flowchart 450 illustrates a more generalizedcalculation for calculating the values for score[j] that takes intoaccount the covariance. Processing begins at the first step 452 where atemporary variable, TMP1, is set equal to zero. Following step 452 is astep 454 where another temporary variable, TMP2, is also set equal tozero. Following the step 454 is a step 456 where an index variable, h,is set equal to one. The index variable h is used to iterate through thecovariant matrixes.

Following the step 456 is a test step 458 which determines if the indexvariable, h, is greater than M, the number of points of the event (andin the patterns of the library). If not, then control transfers from thestep 458 to the step 462 where TMP1 is calculated using the formula:TMP1=TMP1+COVN[h, k]* (RC[k]−NOISE[k])

Following the step 462 is a step 464 where TMP2 is calculated using theformula:TMP2=TMP2+COVJ[h, k]* (RC[k]−FLIB[j, k])

Following the step 464 is a step 466 where the index variable, h, isincremented. Following the step, control transfers back to the step 458,discussed above. Once it is determined at the step 458 that the indexvariable h is greater than M, the number of data points, controltransfers from the step 458 to a step 468 where the value of score[j] iscalculated using the equation:score[j]=score[j]+TMP1*(RC[k]−NOISE[k])+TMP2*(RC[k]−FLIB[j, k])

In some embodiments, it is possible to add the quantity1n(det(COVN)/det(COVJ)) to the final value calculated for score[j](e.g., after the step 406 in the flowchart 400 of FIG. 11), where det isthe determinant (a matrix operation that results in a scalar value). Itis also possible to initialize score[j] to this value at theinitialization step 402.

Note that, in instances where there is no covariance between points ofthe waveforms, then the covariance matrixes will contain zeros except onthe diagonals (the variance). In such a case, the general case discussedin connection with the flowchart 450 of FIG. 12 collapses into thespecial case illustrated in connection with the flowchart 400 of FIG. 11and the equation of the step 408.

FIG. 13A is an example of a test signal on a cable in which the signalis averaged and variance calculated on the returns and showingidentified events of interest. Five events of interest are identified(marked with a “*”) according to the techniques described elsewhereherein and five segments of the signal are indicated as needing to betested. Each segment is subject to pattern recognition against a libraryof events as described above. The process continues until all classes offault have been tested against. FIG. 13B is an example of a displayshowing classification and distance information for the identifiedevents after pattern matching and other processing according to oneembodiment of the invention. As shown in FIG. 13B, two chaffs have beenidentified, a 1 cm chaff at 2.34 meters from the test connector and a 5mm chaff at 3.89 meters from the test connector. The other events arethe test connector, a normal connector and the normal termination.

The shape of the reflected wave is valuable because it reveals thenature and the intensity of the cable mismatch or fault. Diagnostic andprognostic analysis of a cable fault is effected by event classificationpattern recognition and matching techniques described above that areused to compare unclassified events with a stored library of classifiedevents or faults.

Event classification pattern matching utilizes reflection waveformpatterns or profiles of events that are stored in a classification orfault library. Unclassified event profiles are compared with the storedreflection profiles for events such as connectors, terminations andfaults. Generally, faults fall under two categories: Inductive faultsand Capacitive faults. Inductive faults relate to damage to theinsulation due to cuts, nicks and breaks. They are called inductivefaults because the local wire inductance is larger than the nominalwire, resulting in an increase in characteristic impedance. Thecapacitive faults relate to damage characteristic of crimps or bends ina wire, where the insulation is “thinned” and the local capacitanceincreases. This causes a drop in the wire characteristic impedance.

Terminations fall under four basic categories: open, short, inductiveshort and capacitive short. An open termination could reflect a switchor cut in the wire. A short reflects a termination to ground and isimmediately characterized as a fault. Inductive shorts and capacitiveshorts could reflect various hardware terminations, such as a fuel probeand can be used for fault classification. For example, for a wiresupplying a fuel probe, any termination other than a capacitive shortwould be a fault.

Event waveform patterns are stored in the library for identifiableterminations and faults (such as cuts, cracks, chafes, dielectricdegradation, and bad connectors) and utilized to classify anunclassified event of interest. The input waveform profiles of theunclassified events are normalized, corrected for multiple reflections,and converted to reflection coefficients reflecting the settled voltage.These waveform adjustment steps allow wires of different characteristicimpedances to be tested against only one fault library. The use ofsettled voltage is important in order to have only one library. Forexample, if the incident voltage were used instead of the settledvoltage, a 30-Ohm characteristic impedance wire would have a reflectioncoefficient of −0.02. Any event detected on this wire would, withoutusing the settled voltage, be interpreted as a short.

In preferred embodiments, the fault library is generated primarily bytwo methods: empirical testing and analytical modeling.

In the empirical testing method, stored event waveform patterns aregenerated by empirically measuring reflection waveforms for wires havingpurposefully manufactured and identified fault events. The measuredwaveforms are normalized and subjected to other waveform adjustmentsteps to generate a set of reflection profiles that are stored in thefault library and are suitable for comparison with unclassified eventsin wires of differing characteristic impedances.

In one embodiment, a number of wire types are sampled over time and oneor more faults are intentionally introduced into each wire type. Thefaults are classified by severity and type (e.g. termination types,connector, etc.). (See, for example, the general schematic set-up shownin FIG. 20, and the defect embodiments shown in FIGS. 24A-G). Togenerate the stored fault waveform patterns for each fault type,measurements are taken of the reflected waveform profiles for the samefault made multiple times in each particular wire type. The reflectedwaveform profiles are normalized, processed and corrected as describedelsewhere herein. Means values and variances are calculated based on thefault measurements for each wire type. For example, as described above,the variances may be stored in an array VARIANCE[k] which indicates thevariance of each the patterns stored in the fault library FLIB[j, k].

Further, in some embodiments, the covariances associated with each thefault patterns stored in FLIB[j, k] may be calculated and utilized inthe pattern recognition and matching techniques. As described above, thecovariance represents that correlation between each point of the faultlibrary FLIB[j, k1] and each other point FLIB[j, k2], where k1, k2 equalone through M. The covariance may be represented by a two dimensionalsquare matrix, COVJ, for each of the faults in the fault library whereeach entry COVJ[k1, k2] represents the covariance between FLIB[j, k1]and FLIB[j, k2]. In a preferred embodiment, the covariance matrix COVJassociated with each fault is stored as part of the fault library.However, it is contemplated that the covariance matrix can be storedoutside of the fault library in a separate system element that can beutilized as needed in the pattern matching techniques described above.

In analytical modeling, modeling load responses allows efficientmodeling, detection and location of cable faults or defects. The mostgeneral circuit model for cables comprises inductance (L), capacitance(C), shunt conductance (G), and series resistance (R) at each lengthincrement assuming uniform cable properties. FIG. 14 shows a generalGRLC circuit model of an increment cable length Δx.

Applying Kirchoff's law to the circuit yields:

$\begin{matrix}\begin{matrix}{{V_{s}(x)} = {{\left( {{\frac{1}{2}R\;\Delta\; x} + {j\;\frac{1}{2}\; w\; L\;\Delta\; x}} \right)I_{s}} +}} \\{{\left( {{\frac{1}{2}R\;\Delta\; x} + {j\;\frac{1}{2}w\; L\;\Delta\; x}} \right)\left( {I_{s} + {\Delta\; I_{s}}} \right)} + V_{s} + {\Delta\; V_{s}}}\end{matrix} & {{EQUATION}\mspace{14mu}{L1}}\end{matrix}$Letting Δx approach zero yields negligible ΔI_(s), that is,

$\begin{matrix}{\frac{\mathbb{d}V_{s}}{\mathbb{d}x} = {{- \left( {R + {j\; w\; L}} \right)}I_{s}}} & {{EQUATION}\mspace{14mu}{L2}}\end{matrix}$In a similar way, averaging the voltage across the branch and letting Δxapproach zero, yields:

$\begin{matrix}{\frac{\mathbb{d}I_{s}}{\mathbb{d}x} = {{- \left( {G + {j\; w\; C}} \right)}V_{s}}} & {{EQUATION}\mspace{14mu}{L3}}\end{matrix}$These are the counterparts of Maxwell's differential equations(connecting the electric and magnetic fields). They have a well-knownsolution:

$\begin{matrix}\begin{matrix}{{V_{s}(x)} = {V_{0}{\mathbb{e}}^{{- \gamma}\; x}}} \\{{I_{s}(x)} = {\frac{V_{0}}{Z_{0}}{\mathbb{e}}^{{- \gamma}\; x}}} \\{{where},} \\{\gamma = {{\alpha + {j\;\beta}} = \sqrt{\left( {R + {j\; w\; L}} \right)\left( {G + {j\; w\; C}} \right)}}} \\{Z_{0} = \sqrt{\frac{\left( {R + {j\; w\; L}} \right)}{\left( {G + {j\; w\; C}} \right)}}}\end{matrix} & {{{EQUATIONS}\mspace{14mu}{L4}},{L5}}\end{matrix}$With γ being the propagation constant of the cable, α the attenuationconstant of the cable (in Nepers per unit length), β the phase shift (inradians per unit length), and Z₀ being the characteristic impedance ofthe cable. The generator voltage requires a finite time to travel downto a point x. Thus, phase of the voltage moving down the line will lagbehind the generator voltage by an amount β per unit length. The voltagewill also be attenuated by an amount α per unit length due to the seriesresistance and shunt conductance.

Suppose that a “cable” has an air dielectric between its inner and outerconductors. In such case, the velocity of voltage propagation approachesthe speed of light in the cable. Assuming an infinitely long or matched(i.e. has a load equal to its characteristic impedance) cable, thepropagation constant (γ) and the cable characteristic impedance (Z₀)allow the computation of the voltage and the current at any distance xof the cable. When the transmission line is finite in length and notmatched, the above equations are not satisfied unless a second waveoriginating at the load and propagating back toward the generator istaken into account. This reflected wave represents the energy that wasnot absorbed by the load (Z_(L)) as it is different from thecharacteristic impedance (Z₀). The ratio of the reflected wave to theincident wave is called the voltage reflection coefficient (ρ) and isgiven by:

$\begin{matrix}{\rho = \frac{Z_{L} - Z_{0}}{Z_{L} + Z_{0}}} & {{EQUATION}\mspace{14mu}{L6}}\end{matrix}$

The reflection coefficient (ρ) can be seen as the cable “transferfunction” where the input is the incident voltage whereas the output isthe reflected (and not the load) voltages. This notion is very practical(by means of the LaPlace transform) to compute the time response of thesystem under various loads or mismatches, as described below.

In one embodiment, the defect can be accurately modeled as a loadmismatch, and for purposes of modeling, it can be assumed that the loadis known. Knowing incident voltage (V_(i)), cable characteristicimpedance (Z₀), and termination load (Z_(L)) permits the analyticaldetermination of the resulting wave at the source (i.e. incident plusreflected waves), according to the following equation:

$\begin{matrix}{V_{0} = {{\left( {1 + \rho} \right) \times V_{i}} = {\left( \frac{2Z_{L}}{Z_{L} + Z_{0}} \right)V_{i}}}} & {{EQUATION}\mspace{14mu}{L7}}\end{matrix}$

Solving this equation, that involves complex impedance, is a classicproblem and can be solved in many ways. For example, it can beapproached by solving the zero-state response of the system and assuminglinearly superimposed natural and forced responses. It can also besolved by applying the Laplace transform to both sides of the equationand then transforming this product back into the time domain. A simplerand more direct analysis involves evaluating the reflected voltage att=zero and at t=∞ and assuming any transition between these two valuesto be exponential. In any case, it does not matter how the analysis isdone since it will be performed offline to form the system knowledgebase. What matters is the correlation (i.e. degree of similarity)between the reflection of interest and the model under comparison. Inwhat follows, the Laplace transform will be applied to a basic exampleof an RL series model, as shown in FIG. 15. The same approach can beapplied to any other model.

The load impedance in this case is given by,Z _(L) =R+jwL  EQUATION L8Suppose that the incident stimulus is a pulse that can be approximatedby a step function (i.e. E_(i)) during the very short time of theimpulse rise. Applying the Laplace transform to Equation L7 (i.e.working in the p-domain (complex variable p)) yields,

$\begin{matrix}{{V_{0}(p)} = {\left( \frac{2{Z_{L}(p)}}{{Z_{L}(p)} + {Z_{0}(p)}} \right) \times \frac{E_{i}}{p}}} & {{EQUATION}\mspace{14mu}{L9}}\end{matrix}$Where Z_(L)(p) stands for the Laplace transform of Z_(L), that isZ _(L)(p)=R+pL  EQUATION L10For a DC analysis where the characteristic impedance is perceived as atotal impedance (e.g. Z₀=50 ohms), Z₀(p)=Z₀.

Equation L9, yields,

$\begin{matrix}{{V_{0}(p)} = \frac{2{E_{i}\left( {\frac{R}{L} + p} \right)}}{p\left( {p + \frac{R + Z_{0}}{L}} \right)}} & {{EQUATION}\mspace{14mu}{L11}}\end{matrix}$Decompose Equation L11 into simple elements (i.e. zero-poles ratio) thatadmit well behaved Laplace transforms,

$\begin{matrix}{{V_{0}(p)} = {\frac{2{E_{i}\left( {\frac{R}{L} + p} \right)}}{p\left( {p + \frac{R + Z_{0}}{L}} \right)} = {\frac{\alpha}{p} + \frac{\beta}{\left( {p + \frac{R + Z_{0}}{L}} \right)}}}} & {{EQUATION}\mspace{14mu}{L12}}\end{matrix}$Determining the constants α and β is now straightforward. First multiplyboth sides of Equation L12 by the pole of interest (i.e. multiply by pfor α, and

$\left( {p + \frac{R + Z_{0}}{L}} \right)$for β), then let p tend to such poles. For example, to compute α, wemultiply both sides of Equation L12 by p and then let p go to zero. Thisyields,

$\begin{matrix}{\alpha = {\left( \frac{2R}{R + Z_{0}} \right)E_{i}}} & {{EQUATION}\mspace{14mu}{L13}}\end{matrix}$Similarly, multiplying both sides by

$\left( {p + \frac{R + Z_{0}}{L}} \right)$and let β go to

$- \left( \frac{R + Z_{0}}{L} \right)$yields,

$\begin{matrix}{\beta = {\left( \frac{2Z_{0}}{R + Z_{0}} \right)E_{i}}} & {{EQUATION}\mspace{14mu}{L14}}\end{matrix}$Recall that the inverse Laplace transform of a first order 1-pole ratiois given by,

$\begin{matrix}{{L^{- 1}\left\{ \frac{K}{p - p_{0}} \right\}} = {K\;{\mathbb{e}}^{- {(\frac{t}{\tau})}}}} & {{EQUATION}\mspace{14mu}{L15}}\end{matrix}$where τ=1/p₀ is the circuit propagation constant. Thus, the registeredvoltage at the start of the cable is given by inverting Equation L12back into the time domain,

$\begin{matrix}\begin{matrix}{{{V_{0}(t)} = {2E_{i}\left\{ {\frac{R}{R + Z_{0}} + {\frac{Z_{0}}{R + Z_{0}}\;{\mathbb{e}}^{- {(\frac{t}{\tau})}}}} \right\}}},} \\{{{with}\mspace{14mu}\tau} = {L/\left( {R + Z_{0}} \right)}}\end{matrix} & {{EQUATION}\mspace{14mu}{L16}}\end{matrix}$Note that, as mentioned earlier, this could also have been derived usingthe expected voltage at times t=0 and t=∞ and assuming an exponentialdecay between the two instants. In fact, at time t=0 the inductor willnot accept a sudden change in current; it initially looks like aninfinite impedance, and ρ₀=1 at t=0. Thus, V₀(t)|_(t→∞)=(1+ρ₀)E_(i)=2E_(i). Then, the current in L builds upexponentially and its impedance drops toward zero. At t=∞, thereforeZ_(L) is determined only by the value of R (i.e. ρ_(∞)=(R−Z₀)/(R+Z₀)).Hence, V₀(t)|_(t→∞)=(1+ρ_(∞))E_(i)=((2R/(R+Z₀))E_(i). Assuming thevoltage varies between these two limit conditions with a constantτ=L/(R+Z₀) then Equation L13 follows. The constant τ is set at L/(R+Z₀)because it represents the effective resistance seen by the inductor;that is L divided by R+Z₀ (i.e. R is seen in series with Z₀).

The time response of the general response of an R−L mismatch (in a DCcontext) is shown at FIG. 16 (the time origin is supposed when theimpulse first reaches the mismatch). It is known that an inductor inseries with a resistor provide a good approximation of a cable-sensorconnection. Thus, simulating a connection with an RL model is anefficient way to deconvolve the mismatch portion due to the connectionand consider only mismatches of interest (due to cable defects in ourcase). A similar analysis is possible for the case of the parallel R−Ctermination (see Equation L17 and FIG. 17) and parallel R−L termination(see Equation L18 and FIG. 18).

$\begin{matrix}{{V_{0}(t)} = {E_{i} \times \frac{2R}{R + Z_{0}}\left\{ {1 - {\mathbb{e}}^{- {(\frac{t}{\tau})}}} \right\}}} & {{EQUATION}\mspace{14mu}{L17}} \\{{with},{\tau = {\frac{Z_{0}R}{R + Z_{0}}C}}} & \; \\{{V_{0}(t)} = {E_{i} \times \frac{2R}{R + Z_{0}}\left\{ {1 - {\mathbb{e}}^{- {(\frac{t}{\tau})}}} \right\}}} & {{EQUATION}\mspace{14mu}{L18}} \\{{with},{\tau = {\frac{R + Z_{0}}{Z_{0}R}L}}} & \;\end{matrix}$Similarly, such analysis may also be performed for the general RLC case.

In practice, modeling tools such as SPICE can be used to simulatedifferent fault types and generate statistics from these SPICE simulatedfaults. In one example, as shown in FIG. 19, the following events weresimulated. Four non-fault events were developed: Line, Connector Type 1,Connector Type 2, and Connector Type 3. Five fault events weredeveloped: Short Type 1, Short Type 2, Inductive Fault Type 1, InductiveFault Type 2 and Capacitive Fault Type 1. Four Termination events weredeveloped: Open 1, Open 2, Capacitive Short, and Inductive Short. FIG.19 illustrates the reflection waveform patterns with generatedreflection coefficient (rho (ρ)) values for these event types as storedin the fault library.

With modeling tools such as SPICE, upper and lower bounds may be set forcomponent (RLC) values in the simulation of the faults or other events.By appropriately setting these bounds in multiple simulations, themodeling tool allows the generation of multiple points as the RLC valuesare varied. This process allows the generation of variances andcovariances for the simulated faults so as to correspond with expectedsystem noise, much like in the case of empirically derived eventprofiles as described above.

What will now be described are wire diagnostics using jointtime-frequency techniques such as, for example, wavelets and theHilbert-Huang Transform (HHT) for wire defect detection and isolation.Using the joint time-frequency techniques, a stimulus is injected intothe wire of interest as described in connection with, for example,FIG. 1. As described elsewhere herein, reflectometry may be performedusing only one end of a wire under test. The reflected signal thatcorrelates with the wire health and possible defects therein is acquiredfor further processing. As described in following paragraphs,time-frequency techniques that are multi-dimensional may be used todetect and to locate events, such as insulation defects of coaxialcables. Conceptually, time-frequency cells may provide for betterrepresentation of the reflected energy resulting in a sharpidentification of embedded features within the signal of interest. Thejoint time-frequency techniques may be characterized as a 2-dimensionalapproach and may also be referred to as Time-Frequency DomainReflectometry (TFDR). TFDR may be more accurate in identifying andlocating defect-related signatures than a single 1-dimensional approach,including Time Domain Reflectometry (TDR) and Frequency DomainReflectometry (FDR). In connection with the TFDR, wavelets and theHilbert-Huang Transform (HHT) may be used to build time-frequencydistributions of signals of interest.

The TFDR techniques described herein may be used in performing, forexample, event identification processing 104 and event classification asdescribed elsewhere herein in connection with FIG. 2. The output of thecompensation processing 102 of FIG. 2 provides a vector of compensatedreflective voltages obtained at various sampling times that may be usedin TFDR techniques described herein. Subsequently, the output producedfor a wire under test using the TFDR techniques may be compared tobaseline conditions to determine and classify an event occurrence. Itshould be noted as used herein, the term baseline refers to a referenceset of data associated with known wire conditions including, forexample, a baseline data set for a healthy wire condition and a baselinedata set associated with each of one or more particular wire faults,damage states, and the like.

As described elsewhere herein in more detail, wires can be categorizedaccording to many criteria including, for example, type of insulation(e.g. Kapton or Teflon), size and length, or shape (e.g. coaxial ortwisted pair). One embodiment may utilize, for example, a Teflon type ofinsulation in a 0.8-inch-wide, 50-feet-long coaxial cable that mayincluded in an aircraft fuel system. Using reflectometry techniquesdescribed in following paragraphs, the reflected signal from a wire ofinterest is analyzed using time-frequency techniques, such as usingwavelets and HHT.

Existing wire inspection systems using reflectometry analyze signalsexclusively either in the time domain, using TDR techniques, or in thefrequency domain, using FDR techniques. TDR may be employed for signalintegrity verification of transmission lines, primarily in high-speedapplications. The technique of one embodiment includes two main steps.In a first step, a fast rising DC step pulse, such as less than 50 pS,is injected into the wire of interest. Second, the resulting reflectionsare acquired and analyzed. As described elsewhere herein, a perfectwire, such as one with no events, generates no reflections. There aretwo basic types of TDR measurements. The first TDR type, referred to asa single-ended measurement, is performed using a single channel with aTDR step pulse source and a companion receiver for reflection analysis.The second TDR type is a differential measurement performed by injectingtwo signal sources of opposite polarity into adjacent conductors andanalyzing the resulting reflections. As with the single ended technique,each channel consists of one TDR step pulse source and a companionreceiver. The differential technique can reveal additional informationabout parallel conductors inside a common shield including differentialimpedance between conductors.

Traditional TDR methods have been applied to transmission lines with apredictable impedance profile such as coaxial or twisted pair cables. Inthese type of cables, changes in impedance along the conductor(s) maymanifest themselves as discernable changes in the reflection profile.While TDR works very well in identifying opens and shorts along thelength of impedance cables, in the case of damage to the cableinsulating material, the defect is much more difficult to detect withthe TDR technique. Insulation defects usually have little effect on theTDR step pulse and thus have a little or no effect on the reflectionsignature. Use of TDR techniques for detection and location ofinsulation defects presents a challenge in applications, for example,such as in connection with aircraft wiring, in which the wiring mayinclude wiring composed of non-impedance-controlled construction.Furthermore, the effectiveness of TDR diminishes with increased cablelength, due to rise time degradation and attenuation loss.

Frequency Domain Reflectometry (FDR) is similar in principle to the TDRtechnique. FDR uses an RF sweep for wire stimulation, rather than a DCpulse as used in TDR. A portion of the transmitted sweep signal on thecable will be reflected back to the transmitter if the load is not anideal impedance match such as, for example, in the presence of wireevents such as shorts, opens, or any other defect in between. Thereflected energy should be at the same frequency as the incident (sweep)signal, but different in phase. The resulting signal (incident+reflected) appears as standing waves on a frequency sweep. Peaks ofindividual cycles can be translated into distance to the fault through awell-known relation between frequency and distance:

$D = {\frac{c \times V_{op}}{2f} \approx \frac{492 \times V_{op}}{f}}$where D represents the distance to fault, c designates the speed oflight, V_(op) stands for the velocity of propagation of light inside thecable, and f is the frequency of one cycle of the standing wave.Additionally, the peak-to-peak value of the reflection determines themagnitude of the fault. Unlike the TDR technique that uses DC-pulsestimulus thus RF-insensitive, one drawback of the FDR technique is itssensitivity to RF waves.

Accordingly, the TFDR techniques combine aspects of both TDR and FDRthat extract and evaluate failure-related signatures from reflectionsfrom the wire under test. In one embodiment, reference signatures of ahealthy wire and signals associated with particular types of events,such as defects, may be empirically determined, such as by insertinghard failures into a healthy wire, stimulating the wire under test witha predetermined waveform, and then using time-frequency processingtechniques to extract failure-related features from reflected signals.It should be noted that the reference signature of a healthy wire may becompared to those of various events to determined the existence ofdifferent events. The reference signature associated with a healthy wiremay be estimated theoretically from a reflection model or empiricallydetermined from an experimental setup involving a healthy wire.

Referring now to FIG. 20, shown is an example of an embodiment 1000 forgenerating wire stimuli and measuring reflections using the TFDRtechniques. The embodiment 1000 may be used in gathering data aboutspecific types of events and as well as in performing subsequent actualtesting of a wire. The function generator 1002 generates a stimulus forthe wire under test, which in this instance is the coaxial cable 1004.The cable 1004 includes a cable defect 1006 and a simulated wiretermination end 1008 with the cable 1004 connected to common ground1010. The reflection of the cable 1004 is sensed and measured by thedigital scope 1012 and data about the events may be logged as part ofthe data logging unit 1014.

It should be noted that an embodiment may include the function generatoror other components to perform processing steps on the reflectionmeasurement(s) obtained as described herein in order to compensate thereflected signals, such as, for example, in connection with attenuationcompensation and removing unwanted reflections.

Referring now to FIG. 21, shown is an example 1020 of a configurationbased on the general setup described previously in connection with FIG.20. In the example 1020, the stimulus signal is generated, transmitted,and read back automatically by software without human intervention inorder to minimize measurement errors and to correlate abnormalvariations in the reflected signals with wire failures. Theconfiguration 1020 includes a personal computer (PC) 1022 with a GPIB(General Purpose Interface Bus) communication card 1024 and softwarethat controls communications between the GPIB card 1024, the functiongenerator 1002, and the oscilloscope 1012. In this embodiment, thesoftware tool provides control of the function generator and theoscilloscope. A software tool may use any one or more of a variety ofsoftware packages, languages, and the like.

In one embodiment, the PC 1022 may be used in performing otherprocessing steps as described herein, for example, in connection withattenuation processing and removing unwanted reflections.

Referring now to FIG. 22A, shown is one example of a software interface1030. In this embodiment 1030, the LABVIEW software product by NationalInstruments is used. The software interface or graphical user interface(GUI) lets the experimenter select the characteristics of the stimulus,including its shape, frequency, and amplitude, in addition tooscilloscope settings, such as time-base and scaling. Other embodimentsmay use other hardware and/or software and varying configurations thanas described herein.

Referring now to FIG. 22B, shown is a flowchart 1032 of steps of oneembodiment for performing TFDR techniques in connection with identifyingwire events. At step 1034 a, baseline data for a healthy wire isdetermined. At step 1034 b, baseline data for one or more defects of thewire is determined. This may be determined empirically, as described inmore detail elsewhere herein, or using various modeling techniques, asalso described elsewhere herein. The data from steps 1034 a and 1034 bmay be stored, for example, in the library 112 of FIG. 2. At step 1034c, sometime later data is gathered for a wire under test for whichevents, such as a defect, are to be identified. At step 1034 d, acomparison is made between the baseline data and the data obtained forthe wire under test to identify particular events.

Referring now to FIG. 22C, shown is a flowchart 1040 of steps of oneembodiment to gather data about different types of events, such asfaults, in a wire. Flowchart 1040 shows more detail of processing steps1034 a and 1034 b described in connection with FIG. 22B. At step 1042,the length of the cable to be tested is determined. It should be notedthat the cable length may be used in performing compensation processing.At step 1044, an appropriate load (ZL) is then added at the end of thecable to simulate the wire termination 1008. This may be used, forexample, to simulate a sensor or a subsystem to which the cable 1004 isconnected. In one embodiment, a resistor may be used in approximatingresistive loads. To build a small database of baselines for referencesignatures, several measurements of the “healthy” cable may be taken, asat step 1046, prior to damaging the wire for obtaining defect baselinetest case data. At every baseline measurement, the cable may be movedand bent to vary its geometrical configuration. As part of obtainingmeasurements in connection with a healthy cable and also for test eventconditions, an embodiment may also perform processing to remove unwantednoises from the reflective signals, such as, for example, in connectionwith attenuation processing and removing unwanted reflections asdescribed elsewhere herein. At step 1048, a determination is made as towhether all test cases are complete. If so, processing stops. Otherwise,control proceeds to step 1049 where the next test case is determined.Subsequent steps 1050, 1052, and 1054 relate to settings in connectionwith the particular test case of step 1049. At step 1050 interfaceconfiguration is performed, such as in connection with modifying thesettings of the GUI 1030. At step 1052, fault site selection isperformed. At step 1054, cable insulation damaging is performed. At step1056, reflected signal acquisition and data logging are performed. Thedata may be stored, for example, in the library 112 of FIG. 2. Thisprocess is repeated, with increasing damaging conditions, until a givennumber of defects is reached. It should be noted that an embodiment mayperform additional steps or omit one or more of the following inconnection with the particular test case for which data is beinggathered. The foregoing processing steps may be used in connection withempirically obtaining a set of data to be used in comparison steps forwires under test at a later point in time. Similar to step 1046, anembodiment may also include processing steps to remove unwanted noise,such as in connection with attenuation compensation and removingunwanted reflective signals as described elsewhere herein.

In one data gathering phase of one embodiment, four “big” abrasions, forexample as shown in illustration 1070 of FIG. 23, are inflicted on acable in which each subsequent abrasion produced a greater amount ofdamage to the cable than the previous. These abrasions or events ofdamage to the cable indicate a good correlation between extractedfeatures based on the proposed approach described in followingparagraphs and the studied defects. Subsequently, in a second datagathering phase of one embodiment, a broader range of defects areobtained that range in severity from a small cut in the insulation to a7-centimeter-long abrasion.

Referring now to FIG. 24A, shown is an example 1080 of a first defectresulting in a perpendicular cut 10 cm from the end of the cable.Referring now to FIG. 24B, shown is an illustration 1090 of additionaldefects 2-4 made to the cable. These defects include a second defectthat is a 1 cm. longitudinal cut toward the signal source with respectto the cut shown in 1080. The third defect is a perpendicular cut at theend of the cut made in connection with defect #2. The fourth defect is a1 cm. longitudinal cut toward the source with respect to the cut made indefect #3. Referring now to FIG. 24C, shown is an illustration 1100 ofadditional defect 5 made to the cable. Defect 5 is a perpendicular cutmade at the end of the cut of defect #4 that results in opening thecable to the center conductor. Referring now to FIG. 24D, shown is anillustration 1110 of additional defects 6-9 to the cable. Defect #6 is a1 cm. longitudinal cut toward the source with respect to the cute ofdefect #5. Defect #7 is a 3 cm. perpendicular cut at the end of the cutof defect #6. Defect #8 is a 1 cm. longitudinal cut with respect to thecut of defect #7 toward the source. Defect #9 is a perpendicular cut atthe end of the cut associated with defect #8. Referring now to FIG. 24E,shown is an illustration 1120 of defects 10 and 11. Defect #10 is a 1 cmlongitudinal cut with respect to the cut of defect #9. Defect # 11 is aperpendicular cut at the end of the cut associated with defect #10.Referring now to FIG. 24F, shown is an illustration 1130 of defects 12and 13. Defect 12 is a 1 cm. longitudinal cut with respect to the cutassociated with defect #11. Defect #13 is a perpendicular cut withrespect to the cut associated with defect #12. Referring now to FIG.24G, shown is an illustration 1140 of defects 14 and 15. Defect #14 is a1 cm. longitudinal cut with respect to the cut associates with Defect#13. Defect #15 is a perpendicular cut with respect to the cutassociated with Defect #14. It should be noted that other embodimentsmay use different types of events as part of the data gathering processor phase described herein.

An embodiment may use any one or more of a variety of differentwaveforms, including sinusoidal, square, chirp, and pulse types, inconnection with the stimuli signal sent out on the wire in connectionwith detection and isolation of cable insulation defects. Additionally,an embodiment may utilize different wave sizes, total number of samples,and different sampling frequencies.

As used herein, two-dimensional joint time-frequency techniques forsignal processing, such as wavelets, are inherently more efficient thansingle-dimensional time-based or frequency-based techniques. Efficiencyof such multidimensional techniques relates to the ability to capturetransient features exhibiting instantaneous frequency behavior in alimited span of time.

One such two-dimensional TFDR technique utilizes wavelets. Wavelets maybe used to extract sharp features localized in both time and frequency.Such features may relate, for example, to hidden embedded structures ofthe signal of interest due to the adaptive nature of wavelets. In oneembodiment, high frequency analysis may be performed using narrowwindows, and low frequency analysis may be performed using wide windows.As known to those skilled in the art, the term “window” as used hereinmay be described as the time and frequency spectrum over which thedilated and translated mother wavelet is not zero.

It should be noted that wavelet analysis is well suited to deal withnon-stationary data, as in connection with the cable's defect-relatedfeatures.

Wavelet analysis may be either continuous or discrete. ContinuousWavelet Transform (CWT) is a “resemblance” measure calculated bycontinuously shifting a scalable function (i.e. mother wavelet) over thesignal of interest and computing the correlation between two signals,the translated and dilated mother wavelet and the signal under analysis.Use of CWT in an implementation scheme may be computationallyprohibitive in most of real time applications. In one embodiment, a morepractical form of the CWT may be utilized to make the calculation for alimited subset of scales, but at every signal sample.

Discrete Wavelet Transform (DWT) measures the resemblance between themother wavelet and the signal under analysis only on a limited number ofscales (i.e. frequencies) and for a limited number of the signal samplesbased on powers of two. It should be noted that the DWT may be moreefficient and just as accurate as the CWT in most applications. However,the CWT may prove to be superior to the DWT in extracting hiddenfeatures structures embodied in the signal of interest.

Wavelet analysis depends on the wavelet function. Different wavelets maybe appropriate for different applications. It is typically recommendedto select a mother-wavelet function such that the associated digitalfilter has a small order (to speed up the convolution) and the resultinganalysis yields only few nonzero coefficients. In one embodiment inconnection with wire diagnostics, the inventors determined that theMexican hat wavelet exhibited superior performance in featureextraction. An embodiment may prefer to use the CWT in signal analysisbecause it permits continuous tuning of time and frequency resolutions.Although such continuous tuning may be characterized as computationallyexpensive, CWT permits the detection of small variations in thefrequency signature over time. As a first step into characterizing the15 cable faults previously introduced, an embodiment may use thefollowing first of two energy-related features:

$\begin{matrix}{{\rho = \sqrt{\frac{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{{C_{sk} - C_{sk}^{Baseline}}}^{2}}}{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{C_{sk}^{Baseline}}^{2}}}}},} & {{EQUATION}\mspace{14mu}{WV1}}\end{matrix}$where

C_(sk) represents the continuous wavelet coefficients of the signalunder test collected over a time-span of N samples and a time-scale(i.e., frequency) span of S scales; and

C_(sk) ^(Baseline) represents the set of wavelet coefficients of thebaseline signal that is associated with a healthy signature.

In the foregoing EQUATION WV1, s ranges the span of scales with amaximum scale of “S”. As known in the art, scales are parameters used inconnection with wavelet analysis. A scale parameter in connection withwavelet analysis may be characterized as being inversely related to thefrequency of interest. Selection of scale parameter values in anembodiment may vary in accordance with the frequency band of interest,hardware, sampling frequency, type of faults being detected, and thelike.

The differential wavelet energy ratio ρ is proportional to the deviationof the signature energy with respect to the baseline of a healthy wirein the given time-frequency span (N, S). The higher the deviation ρ, themore severe the fault appears in the cable. For example, a ρ value of0.1, means that energy deviation of the faulty signature is about 10%the energy associated with that of a healthy baseline signature.

Referring now to FIG. 24H, shown is a graphical illustration 1145showing the reflections generated by an eight nano-second width pulsesampled at a frequency of 1 GHZ. The illustration 1145 is referencedbelow in connection with other figures.

Referring now to FIG. 25, shown is a graphical illustration 1150 of thevariation of ρ using the Mexican hat wavelet versus the degree of damageon the wire that equates to the order of the fault as determined by theinventors in one embodiment. Illustration 1150 plots the differentialwavelet energy ratio versus fault-sizes computed using the pulsestimulus of the FIG. 24H over a time-span of 0.5 microseconds and afrequency band of 0.1 to 5.6 MHz.

The Defect number is shown in the X axis, ranging from Defect #2 beingthe smallest or least severe defect to Defect #15 being the most severe.These Defect numbers refer to the defects described elsewhere herein.Ideally, ρ should linearly increase with the relative degree of damageon the wire described by the previous fifteen faults. FIG. 18 shows thegap between a failure and a non-failure case. Though not linear, theincreasing trend of ρ versus fault size is in agreement with thedetermination and detection of cable events using the TFDR techniques.

In one embodiment used by the inventors, the following wavelet-basedfeature indicated an increased event detection power and highersensitivity to the size of the failure than the above measure ρ ofEQUATION WV1.

$\begin{matrix}{\delta = \sqrt{\frac{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{{\frac{\partial C_{sk}}{\partial s} - \frac{\partial C_{sk}^{Baseline}}{\partial s}}}^{2}}}{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{\frac{\partial C_{sk}^{Baseline}}{\partial s}}^{2}}}}} & {{EQUATION}\mspace{14mu}{WV2}}\end{matrix}$The feature δ is the local wavelet energy ratio of the signature ofinterest with respect to the baseline of a healthy signature. The“local” nature of wavelet-based signature relates to the partialderivative of the signal energy with respect to the time-scale s (i.e.inverse frequency). It should be noted that “s” and “S” are defined asin connection with the description of EQUATION WV1. The foregoingparameter δ may be characterized as considering irregularities (orentropy) in the distribution of the signal energy. For example, a valueof 0.25 of δ means that the signature under investigation exhibits 25%degree of irregularity more in its energy distribution compared to thatof a healthy or non-defective baseline. This feature may be used todetect the weakest frequency deviations. However, it should be notedthat such a feature may be more sensitive to noise.

Referring now to FIG. 26A, shown is a graphical illustration 1160indicating the variation of δ versus the associated damaging conditiondefect number similar to 1150. Illustration 1160 depicts local waveletenergy ratio versus fault-sizes computed using the pulse stimulus of theFIG. 24H over a time-span of 0 to 0.5 and a frequency band of 0.1 to 5.6MHz. Note that the order of magnitude of δ is about 3 times the order ofmagnitude of ρ (i.e. 0.3 versus 0.1) indicating that in some embodiment,δ may be more effective in detecting events, such as failures, than ρ.

Referring now to FIG. 26B, shown is a flowchart 1165 of steps of oneembodiment summarizing use of the wavelet TFDR technique describedherein for determining wire events for a wire under test. It is assumedthat previous baselines of known wire events and healthy wire conditionshave been determined. At step 1166, the stimulus signal is generated forthe wire under test, and the reflected voltages are obtained and thenmay be compensated. The compensated reflected voltage signals may beobtained, for example, as an output from compensation processing 102 ofFIG. 2. It should be noted that an embodiment may also not performcompensation processing as a previous step depending on the application,amount of noise, and the like. An embodiment may also generate one ormore different types of stimulus signals. For example, one embodimentmay generate pulse signals. An embodiment may also generate a stimulussignal using a wavelet function as described herein. At step 1167, themother wavelet function is selected for processing the compensatedreflective voltages.

At step 1168, the CWT coefficients are determined. At step 1169, thedifferential wavelet energy and local wavelet energy ratio aredetermined. It should be noted that an embodiment may use other featuresthan those of step 1169 in this particular embodiment. At step 1170, theratios for the wire under test are compared to the ratios of known eventconditions, for example, as may be stored in the library 112 of FIG. 2.At step 1171, a determination is made as to whether an event conditionis indicated in accordance with known event data previously obtained andstored in the library. Of so, control proceeds to step 1173 where eventdetails may be output to the user. Otherwise, control proceeds to step1172 where other processing may be performed. Step 1172 processing mayinclude, for example, a message that a wire event or condition could notbe determined.

As described in connection with flowchart 1165, the time-frequencysignatures of the wire under test can be compared to the library oftime-frequency signatures for classification. After canceling the effectof the cable length (e.g. via cable equalization) and other artifacts(e.g. omit multiple reflections via backscattering) 2-D signatures (in atime-frequency plans) can be compared point by point to look for thebest fitting match between the known conditions and the data of the wireunder test. If, for example the best fitting data curve that matches thedata obtained for a wire under test corresponds to a healthy wire, thenthere is no failure. If the best fitting corresponds to a particulartype of failure, such as a “negative bump-type” of failure, then theprocessing of step 1173 may determine an associated cause or diagnosissuch as, for example, that the cause is likely to be a wire short. Itshould be noted that there are many other ways of comparing signaturesfor the final goal of classification, for example, such as those thatmay be applied at a specific limited time span and limited frequencyspectrum rather than comparing each point, or a point everypredetermined interval.

It should be noted that an embodiment may use the techniques ofparametric classification as described elsewhere herein in eventclassification for TFDR techniques. As with any particular techniqueused to analyze a reflective signal, the parameters are determined whichcharacterize each event and may vary with each technique. For example,TFDR techniques may analyze a waveform in the joint time-frequencydomain using parameters in the time and frequency domain in whichamplitude may be a third dimension. The interface defined for this typeof analysis using the parametric classification includes parametersdefined accordingly.

An embodiment may also utilize other wavelet-based features to detectand characterize cable failures and other events. However, the foregoingtwo features were determined to perform best in one embodiment. Anembodiment may include additional features such as, for example, thedigital implementation of the intermittence (i.e. I_(w)(s, t)—EQUATIONWV4) and the time-scale contrast (i.e. E_(w)(s,t)—EQUATION WV3)

$\begin{matrix}{{E_{w}\left( {s,t} \right)} = \frac{C_{w}\left( {s,t} \right)}{\int_{z = 0}^{z = s}{{C_{w}\left( {z,t} \right)}{\mathbb{d}z}}}} & {{EQUATION}\mspace{14mu}{WV3}} \\{{I_{w}\left( {s,t} \right)} = \frac{C_{w}\left( {s,t} \right)}{\left\langle {C_{w}\left( {s,t} \right)} \right\rangle_{t}}} & {{EQUATION}\mspace{14mu}{WV4}}\end{matrix}$

Another TFDR techniques utilizes the HHT technique as described, forexample, in N. Huang, “A New Method for Nonlinear and Nonstationary TimeSeries Analysis: Empirical Mode Decomposition and Hilbert SpectralAnalysis,” Proceeding of SPIE, Vol. 4056, pp. 197-209, Apr. 26-28, 2000,Orlando, Fla. This HHT technique was developed mainly to analyzenonlinear and nonstationary data (e.g. seismic data). Frequencysignatures of nonstationary and nonlinear signals change in time rapidlyand irregularly. Classical spectral analysis techniques, such as theFourier-based analysis, cannot deal efficiently with such data becausesuch spectral analysis techniques are based on the assumption that thedata is either linear, stationary, or both.

An embodiment using the HHT technique decomposes an input signal into afinite and often small number of intrinsic mode functions (IMFs) thatreflect local properties of the signal to which the Hilbert transform(HT) is then applied. The process of data decomposition is calledEmpirical Mode Decomposition (EMD). The Hilbert Transform (HT) is thenapplied to the IMFs. Final presentation of the analysis (i.e. HT of theIMFs) is an energy-frequency-time distribution yielding instantaneousfrequencies may be used to determine meaningful identifications ofembedded features and wire events. Unlike typical spectral analysisapproaches, where the basis functions are fixed and pre-determined, theEMD technique adaptively decomposes the signal into oscillatingcomponents.

As part of EMD, the data is decomposed without reference to a set ofpredetermined basic functions, such as when using, for example, theFourier analysis. For example, the projection basis is built from aprior fixed set of basic functions, such as the case of sine waves forthe Fourier analysis and wavelets for the wavelet analysis. In contrast,the EMD technique decomposes the original signal into a set ofoscillatory modes called Intrinsic Mode Functions (IMF). For a functionto be an IMF, the following two conditions hold true:

-   i) The IMF has the same numbers of zero crossings and extrema;-   ii) The IMF has symmetric envelopes defined by the local maxima and    minima respectively. In other words, the extrema must be symmetric    with respect to the local mean.

The first condition, similar to the sine wave requirement as used withthe Fourier analysis, ensures sharp frequency localization. It issimilar to the narrow-band requirement for a stationary Gaussianprocess. The second condition ensures that the spectral analysis willnot cause undesired frequency artifacts as induced by asymmetricwaveforms.

Following is a pseudo-code description of one embodiment of a processfor generating IMFs from the original signal x(t) representing voltagesat various points in time for different time samples. This process isknown as the sifting process.

1. Initialization

-   -   a) r₀(t)=x(t); Residual initialization    -   b) i=1; Intrinsic Mode Function (IMF) count initialization        2. Extraction of the i^(th) IMF    -   a) j=0; h_(j)(t)=r_(i)(t); Initialize the research of the i^(th)        IMF    -   b) Extract the local minima and maxima of h_(j)(t)    -   c) Interpolate the local extrema by a cubic spline. This step        yields an upper and a lower envelopes for h_(j)(t)    -   d) Compute the mean m_(j)(t) of the envelopes    -   e) h_(j+1)(t)=h_(j)(t)−m_(j)(t)    -   f) If there is “not much” change between h_(j+1)(t) and h_(j)(t)        -   THEN        -   i) Let the i^(th) IMF be h_(j+1)(t); that is            IMF_(i)(t)=h_(j+1)(t)        -   ii) Exit step 2        -   ELSE        -   i) j=j+1        -   ii) Go to b) of step 2            3. Residual Calculation    -   a) r_(i+1)(t)=r_(i)(t)−IMF_(i)(t)    -   b) If r_(j+1)(t) has at least 2 extrema        -   THEN        -   i) i=i+1        -   ii) Go to step 2        -   ELSE        -   i) j=j+1        -   ii) r_(i+1)(t) is the residue        -   iii) Stop the decomposition

One embodiment of the foregoing at step 2f) above used a condition ofhaving the standard deviation between h_(j+1)(t) and h_(j)(t) be atleast 0.3. As used in step 2f), for example, the IF-THEN conditionevaluates to true if the standard deviation between h_(j+1)(t) andh_(j)(t) is not greater than a threshold value. This threshold value inone embodiment may be selected as 0.3 or greater. The foregoingthreshold condition stops an iteration before divergence occurs. It wasfound that threshold values of 0.3 or greater exclude divergence of thealgorithm for the type of data in one embodiment as described herein.Other embodiments may use other thresholds in accordance with the typesof data and applications.

It should also be noted that an implementation of the foregoing mayperform mathematical calculations, such as in connection with standarddeviation, to account for certain conditions, such as a possible divideby zero. One embodiment may determine the standard deviation, SD, as:SD=sum(((h _(j)(t)−h _(j+1)(t))^2)/(h _(j)(t)^2+eps))in which “eps” is some small epsilon value, such as 0.000001, used toavoid a divide by zero error in some instances. It should be noted thatthe particular value selected for eps may vary in accordance with theparticular hardware and/or software and mathematical calculationsincluded in an embodiment.

Additionally, an embodiment include other processing options, such astransformation of the frequency axis over half of the spectrum forbetter visualization of the graphical display of results.

The foregoing converges if the actual IMF has only two extrema (i.e. amonotonic function) or less (i.e. a constant function). In thisinstance, the IMF is the residue of the decomposition. The IMFrepresents the DC part or the trend of the original signal. If N is thetotal number of the intrinsic mode functions then, at the end of theforegoing EMD technique pseudo-code description, the original signal canbe written as:

$\begin{matrix}{{x(t)} = {{\sum\limits_{i = 1}^{N}{{IMF}_{i}(t)}} + {r_{N}(t)}}} & {{EQUATION}\mspace{14mu}{WV5}}\end{matrix}$

The sifting process in the EMD technique is similar to the process ofdilation in the wavelet transform. Each IMF contains lower frequencyoscillations than the previous one just extracted. The first set ofIMFs, designated as being from 1 to K, carry the high frequency contentof the signal. The last portion of IMFs, such as those designated fromN−L to N, carry the low frequency content of the signal.

To illustrate the EMD technique, FIGS. 27A through 27D include graphicalillustrations 1180, 1200, 1220 and 1240 of one example of a voltagesignature along with its 11 intrinsic mode functions. In the foregoing,each IMF has the same number of extrema and zero crossings. Notice alsothat each IMF has symmetric envelopes with respect to the time line.

It should be noted that envelopes, as used herein, may be defined ascurves linking local extrema (i.e. maxima or minima) of a time series,for example, such as may be represented as x(k), k=1 to N. Maxima andminima are points of the curve that satisfy d(k)=x(k+1)−x(k)=0 for theapproximation of the derivative. Typically the number of maxima equalsthe number of minima (plus or minus 1). Depending on the nature of thefirst extremum (either a maximum or a minimum), maxima may be at oddindices (i.e. d(1), d(3), d(5), . . . ) and minima may be on evenindices (i.e. d(2), d(4), d(6), . . . ). There are many ways in whichthese points may be linked together to produce the envelopes such as,for example, cubic spline interpolation.

Once the IMFs are determined, the Hilbert transform may be applied toeach of the IMFs. The Hilbert transform is known by extractinginstantaneous frequency components that can accommodate for data may benonstationary and nonlinear. The Hilbert transform, Y(t), of anarbitrary time series, X(t), is given by:

$\begin{matrix}{{Y(t)} = {\frac{1}{\pi}P\;{\int_{- \infty}^{+ \infty}{\frac{X(\alpha)}{\left( {t - \alpha} \right)}{\mathbb{d}\alpha}}}}} & {{EQUATION}\mspace{14mu}{WV6}}\end{matrix}$where P is a normalizing constant. Equation WV6 defines the Hilberttransform as the convolution of the original signal X(t) with 1/temphasizing the local properties of X(t). Now, consider the followingcomplex signal Z(t)Z(t)=X(t)+iY(t)=A(t)e ^(iθ(t))  EQUATION WV7Hence,

$\begin{matrix}\left\{ \begin{matrix}{{A(t)} = \sqrt{\left( {{X^{2}(t)} + {Y^{2}(t)}} \right)}} \\{{\theta(t)} = {\arctan\left( \frac{Y(t)}{X(t)} \right)}}\end{matrix} \right. & {{EQUATION}\mspace{14mu}{WV8}}\end{matrix}$The polar representation of the original signal X(t), as given byEQUATION WV8, indicates that this representation is the best local fitof an amplitude and phase varying function to X(t). The instantaneousfrequency can be estimated as:

$\begin{matrix}{{f(t)} = {2\;\pi\;\frac{\mathbb{d}{\theta(t)}}{\mathbb{d}t}}} & {{EQUATION}\mspace{14mu}{WV9}}\end{matrix}$Let the instantaneous frequency of the i^(th) IMF be,

$\begin{matrix}{{f_{i}(t)} = {2\;\pi\;\frac{\mathbb{d}{\theta_{i}(t)}}{\mathbb{d}t}}} & {{EQUATION}\mspace{14mu}{WV10}}\end{matrix}$where θ_(i)(t) represents the instantaneous phase of the i^(th) IMF. Ata given instant t, there will be a vector of amplitudes A(t)corresponding to different frequencies of the IMFs (i.e. A(f,t)). Thefinal result, known as the Huang-Hilbert Transform (HHT), is atime-frequency-energy distribution representing the instantaneousHilbert spectrum energy:S _(H)(f,t)=20 log(A ²(f,t))  EQUATION WV11

Data in connection with EQUATION WV11 above may be stored for each ofthe baselines of the healthy wire and different events, such as defectsor faults. This stored data of known events may be compared toadditional analysis data obtained in connection with an actual wireunder test at a later time. The known stored data may be compared to theadditional analysis data to determine the existence/non-existence ofparticular events using any one or more of a variety of differenttechniques as described herein and known in the art. For example, inaddition to the classification techniques described herein, anembodiment may compare a predetermined number of points in each of thetwo data sets using correlation.

The foregoing HHT technique, including the EMD method, is described, forexample, in S. Mallat, “A Theory for Multiresolution SignalDecomposition. The Wavelet Representation,” IEEE Transactions on PatternAnalysis and Machine Intelligence, Vol. 11, No. 7, pp. 674-693, JULY1989; N. Huang, “A new Method for Nonlinear and Nonstationary TimeSeries Analysis: Empirical Mode Decomposition and Hilbert SpectralAnalysis,” Proceeding of SPIE, Vol. 4056, pp. 197-209, 26-28, Apr. 2000,Orlando, Fla.; and Huang, N. E., et al., 1998, “The empirical modedecomposition and the Hilbert spectrum for nonlinear and nonstationarytime series analysis,” Proceedings of the Royal Society London. A, 454,pp. 903-995.

Referring now to FIG. 26C, shown is a flowchart 1174 summarizing stepsof one embodiment of the HHT TFDR technique as described herein. At step1166, the stimulus signal is generated, and the reflected voltagesignals are obtained and then may be compensated. The processing ofgenerating the stimulus signal and compensation is similar to that asdescribed in connection with step 1166 as included in flowchart 1165. Atstep 1175 a, the reflective voltage signals are decomposed using EMDinto one or more IMFs. At step 1175 b, the HT is applied to each IMFproducing a time-frequency-energy distribution representing theinstantaneous Hilbert spectrum energy. At step 1175 c, the HHT of thewire under test is compared to the known event data. At step 1175 d, adetermination is made as to whether the comparison indicates an eventcondition. If so, control proceeds to step 1175 f to output eventdetails. Otherwise, control proceeds to step 1175 e where otherprocessing steps are performed. It should be noted that the known eventdata and comparison techniques that may be utilized in flowchart 1174,such as in steps 1175 c, 1175 d, 1175 e, and 1175 f, are similar tothose as described in connection with flowchart 1165.

The foregoing HHT TFDR technique, as well as the wavelet technique, mayuse one or both of synthesized data and empirical data when determiningbaseline data sets associated with healthy wire conditions and otherevents.

What will now be described are the resulting data sets determined usingthe HHT technique, the classical Fourier analysis and the waveletanalysis technique also described herein. The Fourier analysis isperformed by computing the FFT spectrum energy as follows:S _(F)(f)=20 log(∥ℑ(X(t))∥²)  EQUATION WV12where ℑ(X(t)) is the Fourier transform of the signal X(t).

The wavelet-based energy spectrum is given by:S _(w)(s,t)=20 log(∥W(X(t))∥²)  EQUATION WV13where W(X(t)) is the (Haar) wavelet transform (WT) and s is the scalevariable that is inversely proportional to the frequency. As an exampleof the different baseline data sets and how the foregoing FFT, waveletand HHT techniques may be used to each graphically characterize anevent, consider the test signal illustrated in the graph 1300 of FIG.28A. The graph 1300 illustrates a sine wave with a frequency switch atthe middle of the time span.

Referring now to FIG. 28B, shown is an illustration 1320 of the Fourierbased energy spectrum using the signal of 1300. The illustration 1320shows the existence of the two harmonics that form the signal. However,the Fourier-based spectrum provides no indication at what time does theswitch on frequency happened.

Referring now to FIG. 28C, shown is a graphical illustration 1340 of thewavelet transform of the signal 1300. The illustration 1340 does showthe time of the frequency switch, however it does not clearly identifythe frequency. In fact, referring to 1340, the frequency signature isspread over the frequency axis.

Referring now to FIG. 28D, shown is a graphical illustration 1360 of theHHT providing sharp localization of the spectrum in both time andfrequency. It should also be noted that the HHT may be displayed as 3-Dmesh where the energy is presented versus time and frequency. Asillustrated herein, in some applications, the HHT technique may providebetter results and be preferred over the wavelet technique.Additionally, more that one technique may be used in connection withidentifying particular types of events.

It should be noted that an embodiment may prefer to use the HHTtechnique and/or the wavelet technique, as well as other TFDR techniquesin accordance with the type of signals being analyzed. For example, ifthe signal under analysis may be characterized as non-linear andnon-stationary, use of the HHT technique may be preferred over thewavelet techniques described herein.

Using the TFDR techniques, such as the wavelet and HHT techniquesdescribed herein, event features, such as those related the fault sizeand location, may be extracted. The output of TFDR processing for a wireunder test may be compared to baseline data, such as may be stored inthe library 112 of FIG. 2, to perform event identification andclassification.

In connection with the HHT technique, various intrinsic mode functionsare generated and have their Hilbert transform computed. One embodimentmay use software packages, such as the HHT Toolbox from PrincetonSatellite Systems to implement the techniques described herein. Otherembodiments may use other combinations of hardware and/or software.

While the invention has been disclosed in connection with variousembodiments, modifications thereon will be readily apparent to thoseskilled in the art. Accordingly, the spirit and scope of the inventionis set forth in the following claims.

1. A method of determining an event on a wire comprising: receiving asignal on the wire; performing compensation processing of said signalproducing a compensated signal, wherein said compensation processingincludes performing attenuation compensation in accordance with amultivariate function that depends simultaneously on frequency and alength of a conductor on which said signal propagates; performing eventidentification processing of said compensated signal to identify atleast one event; and classifying said at least one event using a libraryof circuit models, wherein, if said at least one event indicates a faultcondition, said classifying includes classifying a type of faultcorresponding to said at least one event, wherein said classifyingincludes comparing information about said compensated signal to at leastone set of data representing a first type of wire defect, said at leastone set of data being generated using a cable model simulating saidfirst type of wire defect, wherein if said at least one event indicatesa fault condition, providing a result regarding said fault conditionincluding at least one of providing said result to a user display,providing said result to storage, and providing an indicator that afault has been detected.
 2. The method of claim 1, further comprising:compensating said signal to remove unwanted reflective components due toinverse scattering producing a first adjusted signal; and performingsaid attenuation compensation on said first adjusted signal.
 3. Themethod of claim 2, further comprising: associating event data with atleast one predetermined event prior to said classifying, wherein saidclassifying uses said event data.
 4. The method of claim 3, wherein saidat least one predetermined event includes at least one of: a connector,a cut, a nick, a crimp, damage to wire insulation due to age, damage towire insulation due to coupling of the wire with another element.
 5. Themethod of claim 4, further comprising: determining said event data byempirical analysis.
 6. The method of claim 4, further comprising:storing said event data in a library.
 7. The method of claim 3, whereinsaid at least one predetermined event includes at least one of an openor a short.
 8. The method of claim 2, wherein said attenuationcompensation is a function of frequency and an amount of time saidsignal has traveled in said wire.
 9. The method of claim 2, wherein saidattenuation compensation is a function of frequency.
 10. The method ofclaim 2, wherein said attenuation compensation is a function of time.11. The method of claim 1, wherein said signal is a reflective signaland the method further comprising: analyzing said reflective signal inaccordance with at least one joint time-frequency domain reflectometrytechnique.
 12. The method of claim 11, further comprising: sending asignal on the wire wherein said signal is one of: an impulse signal anda predetermined wavelet.
 13. The method of claim 12, further comprising:determining at least one characteristic of said reflective signal inaccordance with a predetermined wavelet; and using said at least onecharacteristic in said event identification and said classifying. 14.The method of claim 1, further comprising: determining a firstderivative of said signal; and identifying at least one peak of saidfirst derivative exceeding a predetermined threshold as an event. 15.The method of claim 1, wherein said cable model is a circuit model of acable.
 16. The method of claim 1, further including: processing saidcompensated signal using a cable model which is empirically determinedusing one or more measurements associated with a non-damaged cable. 17.A device that determines an event on a wire comprising: a receiver thatreceives a signal on the wire; and a processor that performscompensation processing of the signal producing a compensated signal,performs event identification processing of the compensated signal toidentify at least one event, and that classifies said at least one eventusing a library of circuit models, wherein, if said at least one eventindicates a fault condition, classifying of said at least one eventincludes classifying a type of fault corresponding to said at least oneevent, said classifying includes comparing information about saidcompensated signal to at least one set of data representing a first typeof wire defect, said at least one set of data being generated using acable model simulating said first type of wire defect, wherein if saidat least one event indicates a fault condition, said processor providesa result regarding said fault condition including at least one ofproviding said result to a user display, providing said result tostorage, and providing an indicator that a fault has been detected,wherein said compensation processing includes performing attenuationcompensation in accordance with a multivariate function that dependssimultaneously on frequency and a length of a conductor on which saidsignal propagates.
 18. The device of claim 17, wherein said processorcompensates said signal to remove unwanted reflective components due toinverse scattering producing a first adjusted signal and performs saidattenuation compensation on said first adjusted signal.
 19. The deviceof claim 18, further comprising: a data storage element containing eventdata, wherein said processor associates said event data with at leastone predetermined event prior to said classifying, wherein saidclassifying uses said event data.
 20. The device of claim 19, whereinsaid at least one predetermined event includes at least one of: aconnector, a cut, a nick, a crimp, damage to wire insulation due to age,damage to wire insulation due to coupling of the wire with anotherelement.
 21. The device of claim 20, wherein said processor determinessaid event data by empirical analysis.
 22. The device of claim 19,wherein said at least one predetermined event includes at least one ofan open or a short.
 23. The device of claim 18, wherein said attenuationcompensation is a function of frequency and an amount of time saidsignal has traveled in said wire.
 24. The device of claim 18, whereinsaid attenuation compensation is a function of frequency.
 25. The deviceof claim 17, wherein said signal is a reflective signal and saidprocessor analyzes said reflective signal in accordance with at leastone joint time-frequency domain reflectometry technique.
 26. The deviceof claim 25, further comprising: a signal generator that generates atleast one of: an impulse signal and a predetermined wavelet.
 27. Thedevice of claim 26, wherein the processor determines at least onecharacteristic of said reflective signal in accordance with apredetermined wavelet and wherein said at least one characteristic isused in said event identification and said classifying.
 28. The deviceof claim 17, wherein said processor determines a first derivative ofsaid signal and identifies at least one peak of said first derivativeexceeding a predetermined threshold as an event.
 29. The device of claim17, wherein said cable model is a circuit model of a cable.
 30. Thedevice of claim 17, wherein said processor processes said compensatedsignal using a cable model which is empirically determined using one ormore measurements associated with a non-damaged cable.
 31. A computerreadable medium comprising code stored thereon that determines an eventon a wire, the computer readable medium comprising: executable code thatreceives a signal on the wire; executable code that performscompensation processing of the signal producing a compensated signal,wherein said executable code that performs compensation processingincludes executable code that performs attenuation compensation inaccordance with a multivariate function that depends simultaneously onfrequency and a length of a conductor on which said signal propagates;executable code that performs event identification processing of thecompensated signal to identify at least one event; and executable codethat classifies said at least one event using a library of circuitmodels, wherein, if said at least one event indicates a fault condition,said executable code that classifies includes code that classifies atype of fault corresponding to said at least one event, wherein saidexecutable code that classifies includes code that compares informationabout said compensated signal to at least one set of data representing afirst type of wire defect, said at least one set of data being generatedusing a cable model simulating said first type of wire defect, whereinif said at least one event indicates a fault condition, providing aresult regarding said fault condition including at least one ofproviding said result to a user display, providing said result tostorage, and providing an indicator that a fault has been detected. 32.The computer readable medium of claim 31, further comprising: executablecode that compensates said signal to remove unwanted reflectivecomponents due to inverse scattering producing a first adjusted signal;and said executable code that performs attenuation compensation performsattenuation compensation on said first adjusted signal.
 33. The computerreadable medium of claim 32, further comprising: executable code thatassociates event data with at least one predetermined event prior toclassifying, wherein classifying uses said event data.
 34. The computerreadable medium of claim 33, wherein said at least one predeterminedevent includes at least one of: a connector, a cut, a nick, a crimp,damage to wire insulation due to age, damage to wire insulation due tocoupling of the wire with another element.
 35. The computer readablemedium of claim 34, further comprising: executable code that determinessaid event data by empirical analysis.
 36. The computer readable mediumof claim 34, further comprising: executable code stores said event datain a library.
 37. The computer readable medium of claim 33, wherein saidat least one predetermined event includes at least one of an open or ashort.
 38. The computer readable medium of claim 31, wherein said signalis a reflective signal and computer program product is furthercomprising: executable code that analyzes said reflective signal inaccordance with at least one joint time-frequency domain reflectometrytechnique.
 39. The computer readable medium of claim 38, furthercomprising: executable code that sends a signal on the wire wherein saidsignal is one of: an impulse signal and a predetermined wavelet.
 40. Thecomputer readable medium of claim 39, further comprising: executablecode that determines at least one characteristic of said reflectivesignal in accordance with a predetermined wavelet; and executable codethat uses said at least one characteristic in said event identificationand said classifying.
 41. The computer readable medium of claim 32,wherein said attenuation compensation is a function of frequency and anamount of time said signal has traveled in said wire.
 42. The computerreadable medium of claim 32, wherein said attenuation compensation is afunction of frequency.
 43. The computer readable medium of claim 32,further comprising: executable code that determines a first derivativeof said signal; and executable code that identifies at least one peak ofsaid first derivative exceeding a predetermined threshold as an event.44. The computer readable medium of claim 32, wherein said attenuationcompensation is a function of time.
 45. The computer readable medium ofclaim 31, wherein said cable model is a circuit model of a cable. 46.The computer readable medium of claim 28, further comprising executablecode that processes said compensated signal using a cable model which isempirically determined using one or more measurements associated with anon-damaged cable.
 47. A method for detecting an event on a wirecomprising: determining a plurality of polynomials, each of saidpolynomials fitting a portion of data points representing a receivedwaveform, wherein said each polynomial is a localized curve fitting ofsaid portion of data points that approximates values of the data pointsin the portion; determining a first derivative for each of saidplurality of polynomials; evaluating said first derivative of each ofsaid plurality of polynomials at data points representing said receivedwaveform; detecting an event using said first derivative of each of saidplurality of polynomials; and providing a result regarding said event,said providing including at least one of providing said result to a userdisplay, providing said result to storage, and providing an indicatorregarding said result.
 48. The method of claim 47, further comprising:determining an event detection threshold.
 49. The method of claim 48,further comprising: determining at least one peak using said firstderivatives that exceeds said event detection threshold; storing datacorresponding to said at least one peak; and classifying said data asone of a plurality of events.
 50. The method of claim 47, furthercomprising: compensating said received waveform prior to saiddetermining a plurality of polynomials.
 51. The method of claim 47,wherein the event is one of: a connector, a cut, a nick, a crimp, damageto wire insulation due to age, damage to wire insulation due to couplingof the wire with another element.
 52. The method of claim 47, furthercomprising: storing data of said waveform in accordance with said eventdetected.
 53. The method of claim 47, further comprising: classifyingsaid event.
 54. The method of claim 47, wherein the event includes atleast one of an open or a short.
 55. A computer readable mediumcomprising code stored thereon for detecting an event on a wire, thecomputer readable medium comprising: executable code that determines aplurality of polynomials, each of said polynomials fitting a portion ofdata points representing a received waveform, wherein said eachpolynomial is a localized curve fitting of said portion of data pointsthat approximates values of the data points in the portion; executablecode that determines a first derivative for each of said plurality ofpolynomials; executable code that evaluates said first derivative ofeach of said plurality of polynomials at data points representing saidreceived waveform; executable code that detects an event using saidfirst derivative of each of said plurality of polynomials; andexecutable code that provides a result regarding said event including atleast one of providing said result to a user display, providing saidresult to storage, and providing an indicator that a fault has beendetected.
 56. The computer readable medium of claim 55, furthercomprising: executable code that determines an event detectionthreshold.
 57. The computer readable medium of claim 56, furthercomprising: executable code that determines at least one peak using saidfirst derivatives evaluated that exceed said event detection threshold;executable code that stores data corresponding to said at least onepeak; and executable code that classifies said data as one of aplurality of events.
 58. The computer readable medium of claim 55,further comprising: executable code that compensates said receivedwaveform prior to said determining a plurality of polynomials.
 59. Thecomputer readable medium of claim 55, wherein the event is one of: aconnector, a cut, a nick, a crimp, damage to wire insulation due to age,damage to wire insulation due to coupling of the wire with anotherelement.
 60. The computer readable medium of claim 55, furthercomprising: executable code that stores data of said waveform inaccordance with said event detected.
 61. The computer readable medium ofclaim 55, further comprising: executable code that classifies saidevent.
 62. The computer readable medium of claim 55, wherein the eventincludes at least one of an open or a short.
 63. A method of processinga signal received on a wire comprising: receiving said signal;compensating said signal to remove unwanted reflections caused by adefect in said wire producing a compensated signal; analyzing saidcompensated signal to determine information about said defect; receivinga plurality of reflective voltages and a plurality of incident voltages,wherein at a measured voltage at a time is equal to a sum of areflective voltage and an incident voltage at a the time; and adjustingeach of said plurality of reflective voltages and said plurality ofincident voltages determined at a point to remove unwanted reflectionsfrom the point to the end of the wire, wherein there are N incidentvoltages and N corresponding reflective voltages, and the method furthercomprising: initializing a first row of an N×N matrix, D, with said Nincident voltages; initializing a first row of an N×N matrix, U, withsaid N reflective voltages; determining reflection coefficientscorresponding to said N incident and N reflective voltages; determiningtransmission coefficients corresponding to said reflection coefficients;for each element of row ii of matrix D, ii=2 to N, determiningD(ii,jj)=(D(i,j)−r(ii)*U(i,jj))/s(ii), where i=1 to N−1, j=i to N−1,jj=j+1, s(ii) is a transmission coefficient at time ii, r(ii) is areflection coefficient at a time ii; and for each element of row ii ofmatrix U, determining U(ii,jj)=(−r(ii)*D(i,j)+U(i,jj))/s(ii), whereindiagonals of matrix D, D[t,t], t=1 to N, are N adjusted incidentvoltages at each time t, Vinc,adj(t).
 64. The method of claim 63,further comprising: determining adjusted reflective voltages at eachtime t, Vrefl,adj (t), as:Vrefl,adj(t)=(Z(t+1)−Z ₀)/(Z ₀ +Z(t+1))*Vinc,adj(t)+Vinc,adj(t), whereZ₀ is a characteristic impedance of the wire,Z(t+1)=Z(t)*(1+r(t))/(1−r(t)).
 65. The method of claim 64, furthercomprising: performing error correction by assigning each of saidreflection coefficients to zero if said each reflection coefficient isless than a predetermined threshold.
 66. The method of claim 65, whereinsaid predetermined threshold is a value equal to a product of threetimes a standard deviation of a noise level.
 67. A computer readablemedium comprising code stored thereon that processes a signal receivedon a wire, the computer readable medium comprising: executable code thatreceives said signal; executable code that compensates said signal toremove unwanted reflections caused by a defect in said wire producing acompensated signal; and executable code that analyzes said compensatedsignal to determine information about said defect; executable code thatreceives a plurality of reflective voltages and a plurality of incidentvoltages, wherein at a measured voltage at a time is equal to a sum of areflective voltage and an incident voltage at a the time; and executablecode that adjusts each of said plurality of reflective voltages and saidplurality of incident voltages determined at a point to remove unwantedreflections from the point to the end of the wire, wherein there are Nincident voltages and N corresponding reflective voltages, and thecomputer program product further comprising: executable code thatinitializes a first row of an N×N matrix, D, with said N incidentvoltages; executable code that initializes a first row of an N×N matrix,U, with said N reflective voltages; executable code that determinesreflection coefficients corresponding to said N incident and Nreflective voltages; executable code that determines transmissioncoefficients corresponding to said reflection coefficients; executablecode that, for each element of row ii of matrix D, ii=2 to N, determinesD(ii,jj)=(D(i,j)−r(ii)*U(i,jj))/s(ii), where i=1 to N−1,j=i to N−1,jj=j+1, s(ii) is a transmission coefficient at time ii, r(ii) is areflection coefficient at a time ii; and executable code that, for eachelement of row ii of matrix U, determinesU(ii,jj)=(−r(ii)*D(i,j)+U(i,jj))/s(ii), wherein diagonals of matrix D,D[t,t], t=1 to N, are N adjusted incident voltages at each time t,Vinc,adj(t).
 68. The computer readable medium of claim 67, furthercomprising: executable code that determines adjusted reflective voltagesat each time t, Vrefl,adj(t), as:Vrefl,adj(t)=(Z(t+1)−Z ₀)/(Z ₀ +Z(t+1))*Vinc,adj(t)+Vinc,adj(t), whereZ₀ is a characteristic impedance of the wire,Z(t+1)=Z(t)*(1+r(t))/(1−r(t)).
 69. The computer readable medium of claim68, further comprising: executable code that performs error correctionby assigning each of said reflection coefficients to zero if said eachreflection coefficient is less than a predetermined threshold.
 70. Thecomputer readable medium of claim 69, wherein said predeterminedthreshold is a value equal to a product of three times a standarddeviation of a noise level.
 71. A method of detecting events on a wirecomprising: determining at least one set of reference data indicating awire event; sending an impulse signal on the wire; obtaining areflective return signal corresponding to said impulse signal; analyzingsaid reflective signal in accordance with at least one jointtime-frequency domain reflectometry technique; determining at least onecharacteristic of said reflective signal in accordance with apredetermined wavelet; performing wavelet analysis using a continuouswavelet transform; determining ρ as a feature of said reflective signalwherein p is a differential wavelet energy ratio ρ proportional to thedeviation of a signature energy with respect to a baseline of said wirein a healthy condition for a given time-frequency span; and providing aresult regarding said reflective signal including at least one ofproviding said result to a user display, providing said result tostorage, and providing an indicator of said result.
 72. The method ofclaim 71, wherein ρ is represented as:$\rho = \sqrt{\frac{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{{C_{sk} - C_{sk}^{Baseline}}}^{2}}}{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{C_{sk}^{Baseline}}^{2}}}}$in which: C_(sk) represents continuous wavelet coefficients of a signalunder test collected over a time-span of N samples and a time-scale spanof S scales, wherein said scales are parameters used in performing saidwavelet analysis; and C_(sk) ^(Baseline) represents a set of waveletcoefficients of a baseline signal associated with a healthy signature.73. The method of claim 72, further comprising: determining δ as afeature of said reflective signal, wherein δ is a local wavelet energyratio of a signature of interest with respect to a baseline of a healthysignature, said local nature of said signatures relating to a partialderivative of signal energy with respect to a time-scale correspondingto an inverse frequency of said signal energy.
 74. The method of claim73, wherein δ is represented as:$\delta = \sqrt{\frac{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{{\frac{\partial C_{sk}}{\partial s} - \frac{\partial C_{sk}^{Baseline}}{\partial s}}}^{2}}}{\sum\limits_{k = 1}^{N}{\sum\limits_{s = 1}^{S}{\frac{\partial C_{sk}^{Baseline}}{\partial s}}^{2}}}}$in which ∂ represents a partial derivative.
 75. The method of claim 71,wherein increasing values of ρ, are associated with increasing severityof wire events detected.
 76. A method for creating a classificationlibrary for classifying defects in connection with cable analysis,comprising: generating a reflection waveform pattern of an event;processing said reflection waveform pattern to produce a classificationreflection waveform pattern; storing said classification reflectionwaveform pattern in said classification library, said classificationlibrary including classification reflection waveform patternscorresponding to different types of possible fault conditions, whereinsaid classification library includes at least one set of datarepresenting a first type of wire defect, said at least one set of databeing generated using a cable model simulating said first type of wiredefect.
 77. The method of claim 76, wherein said event is selected fromthe group consisting of: a fault, a connector, and a termination. 78.The method of claim 76, wherein generating a reflection waveform patternincludes: creating a specified type of fault in a cable of a specifiedtype; producing a voltage waveform signal in said cable; identifying areflected voltage waveform signal portion for said specified type offault; and converting said reflected voltage waveform signal portioninto a reflection waveform pattern.
 79. The method of claim 76, whereinsaid model is an analytical model, and generating a reflection waveformpattern includes: simulating said event utilizing said analytical model;and generating a reflection waveform pattern from said analytical model.80. A computer readable medium comprising code stored thereon thatcreates a classification library for classifying defects in connectionwith cable analysis, the computer readable medium comprising: executablecode that generates a reflection waveform pattern of an event;executable code that processes said reflection waveform pattern toproduce a classification reflection waveform pattern; and executablecode that stores said classification reflection waveform pattern in saidclassification library, said classification library includingclassification reflection waveform patterns corresponding to differenttypes of possible fault conditions, wherein said classification libraryincludes at least one set of data representing a first type of wiredefect, said at least one set of data being generated using a cablemodel simulating said first type of wire defect.
 81. The computerreadable medium of claim 80, wherein said event is selected from thegroup consisting of: a fault, a connector, and a termination.
 82. Thecomputer readable medium of claim , wherein said executable code thatgenerates a reflection waveform pattern of an event, includes:executable code that produces a voltage waveform signal in said cable;executable code that identifies a reflected voltage waveform signalportion for a specified type of fault; executable code that convertssaid reflected voltage waveform signal portion into a reflectionwaveform pattern.
 83. The computer readable medium of claim 80, whereinsaid model is an analytical model and said executable code thatgenerates a reflection waveform pattern of an event, includes:executable code that simulates said event utilizing said analyticalmodel; and executable code that generates a reflection waveform patternfrom said analytical model.
 84. A method for creating a classificationlibrary for cable analysis, comprising: generating a reflection waveformpattern of an event, wherein generating a reflection waveform patternincludes: creating a specified type of fault in a cable of a specifiedtype; producing a voltage waveform signal in said cable; identifying areflected voltage waveform signal portion for said specified type offault; and converting said reflected voltage waveform signal portioninto a reflection waveform pattern; processing said reflection waveformpattern to produce a classification reflection waveform pattern; storingsaid classification reflection waveform pattern; providing a pluralityof voltage waveform signals; calculating a mean value reflectionwaveform pattern from at least two normalized and corrected reflectionwaveform patterns; calculating a variance array that includes varianceinformation of said least two normalized reflection waveform patternscompared with said mean value reflection waveform pattern; and storingsaid variance array so as to be accessible with said classificationreflection waveform pattern.
 85. The method of claim 84, furthercomprising: generating a covariance matrix using information in saidvariance array; storing said covariance matrix so as to be accessiblewith said classification reflection waveform pattern.
 86. A computerreadable medium comprising code stored thereon that creates aclassification library for cable analysis, comprising: executable codethat generates a reflection waveform pattern of an event, wherein saidexecutable code that generates a reflection waveform pattern of anevent, includes: executable code that produces a voltage waveform signalin said cable; executable code that identifies a reflected voltagewaveform signal portion for a specified type of fault; and executablecode that converts said reflected voltage waveform signal portion into areflection waveform pattern; executable code that processes saidreflection waveform pattern to produce a classification reflectionwaveform pattern; executable code that stores said classificationreflection waveform pattern; executable code that calculates a meanvalue reflection waveform pattern from at least two normalized andcorrected reflection waveform patterns; executable code that calculatesa variance array that includes variance information of said least twonormalized reflection waveform patterns compared with said mean valuereflection waveform pattern; and executable code that stores saidvariance array so as to be accessible with said classificationreflection waveform pattern.
 87. The computer readable medium of claim86, further comprising: executable code that generates a covariancematrix using information in said variance array; and executable codethat stores said covariance matrix so as to be accessible with saidclassification reflection waveform pattern.
 88. A method for detectingan event on a wire comprising: determining a plurality of polynomials,each of said polynomials fitting a portion of data points representing areceived waveform; determining a first derivative for each of saidplurality of polynomials; evaluating said first derivative of each ofsaid plurality of polynomials at data points representing said receivedwaveform; and detecting an event using said first derivative of each ofsaid plurality of polynomials, wherein said portion of data points hasN+M+1 data points, N representing a number of data points prior to afirst one of said data points included in said portion, M representing anumber of data points after said first one of said data points includedin said portion, and the method further comprising: determining a firstof said plurality of polynomials in accordance with said N+M+1 datapoints; and providing a result regarding said event including at leastone of providing said result to a user display, providing said result tostorage, and providing an indicator of said result.
 89. The method ofclaim 88, further comprising: determining a first derivative of saidfirst polynomial; and evaluating said first derivative at said first oneof said data points included in said portion.
 90. A computer readablemedium comprising code stored thereon for detecting an event on a wire,the computer readable medium comprising: executable code that determinesa plurality of polynomials, each of said polynomials fitting a portionof data points representing a received waveform; executable code thatdetermines a first derivative for each of said plurality of polynomials;executable code that evaluates said first derivative of each of saidplurality of polynomials at data points representing said receivedwaveform; and executable code that detects an event using said firstderivative of each of said plurality of polynomials, wherein saidportion of data points has N+M+1 data points, N representing a number ofdata points prior to a first one of said data points included in saidportion, M representing a number of data points after said first one ofsaid data points included in said portion, and the computer readablemedium further comprising: executable code that determines a first ofsaid plurality of polynomials in accordance with said N+M+1 data points;and executable code that provides a result regarding said eventincluding at least one of providing said result to a user display,providing said result to storage, and providing an indicator of saidresult.
 91. The computer readable medium of claim 90, furthercomprising: executable code that determines a first derivative of saidfirst polynomial; and executable code that evaluates said firstderivative at said first one of said data points included in saidportion.
 92. A method of determining an event on a wire comprising:receiving a signal on the wire; performing compensation processing ofsaid signal producing a compensated signal; performing eventidentification processing of said compensated signal to identify atleast one event; classifying said at least one event; determining aplurality of polynomials, each of said polynomials locally fitted to aportion of data points defining a portion of said signal, each of saidportion of data points being including a kernel point; determining aplurality of first derivatives of said plurality of polynomials;evaluating each of said plurality of first derivatives at acorresponding kernel point producing a plurality of evaluated firstderivatives; determining said at least one event using said plurality ofevaluated first derivatives; and providing a result regarding said atleast one event including at least one of providing said result to auser display, providing said result to storage, and providing anindicator regarding said result.
 93. A computer readable mediumcomprising code stored thereon that determines an event on a wire, thecomputer readable medium comprising: executable code that receives asignal on the wire; executable code that performs compensationprocessing of the signal producing a compensated signal; executable codethat performs event identification processing of the compensated signalto identify at least one event; executable code that classifies said atleast one event; executable code that determines a plurality ofpolynomials, each of said polynomials locally fitted to a portion ofdata points defining a portion of said signal, each of said portion ofdata points being including a kernel point; executable code thatdetermines a plurality of first derivatives of said plurality ofpolynomials; executable code that evaluates each of said plurality offirst derivatives at a corresponding kernel point producing a pluralityof evaluated first derivatives; executable code that determines said atleast one event using said plurality of evaluated first derivatives; andexecutable code that provides a result regarding said at least one eventincluding at least one of providing said result to a user display,providing said result to storage, and providing an indicator of saidresult.
 94. A device that determines an event on a wire comprising: areceiver that receives a signal on the wire; and a processor thatperforms compensation processing of the signal producing a compensatedsignal, performs event identification processing of the compensatedsignal to identify at least one event, and that classifies said at leastone event, wherein said processor determines a plurality of polynomials,each of said polynomials locally fitted to a portion of data pointsdefining a portion of said signal, each of said portion of data pointsbeing including a kernel point, said processor determines a plurality offirst derivatives of said plurality of polynomials, said processorevaluates each of said plurality of first derivatives at a correspondingkernel point producing a plurality of evaluated first derivatives, andsaid processor determines said at least one event using said pluralityof evaluated first derivatives, wherein said processor provides a resultregarding said at least one event including at least one of providingsaid result to a user display, providing said result to storage, andproviding an indicator of said result.
 95. A method for creating aclassification library for cable analysis, comprising: generating areflection waveform pattern of an event; processing said reflectionwaveform pattern to produce a classification reflection waveformpattern; and storing said classification reflection waveform pattern,wherein processing said reflection waveform pattern includes normalizingand correcting said reflection waveform pattern to produce saidclassification reflection waveform pattern.
 96. A method for creating aclassification library for cable analysis, comprising: generating areflection waveform pattern of an event, wherein generating a reflectionwaveform pattern includes: simulating said event utilizing an analyticalmodel; and generating a reflection waveform pattern from said analyticalmodel; processing said reflection waveform pattern to produce aclassification reflection waveform pattern; storing said classificationreflection waveform pattern; adjusting component values of saidanalytical model prior to resimulating said event utilizing ananalytical model and regenerating a reflection waveform pattern fromsaid analytical model; generating a variance array corresponding to theadjustment of said component values in said analytical model; storingsaid variance array so as to be accessible with said classificationreflection waveform pattern.
 97. A computer readable medium comprisingcode stored thereon that creates a classification library for cableanalysis, the computer readable medium comprising: executable code thatgenerates a reflection waveform pattern of an event; executable codethat processes said reflection waveform pattern to produce aclassification reflection waveform pattern; and executable code thatstores said classification reflection waveform pattern, wherein saidexecutable code that processes said reflection waveform pattern toproduce a classification reflection waveform pattern includes executablecode that normalizes and corrects said reflection waveform pattern toproduce said classification reflection waveform pattern.
 98. A computerreadable medium that creates a classification library for cableanalysis, comprising: executable code that generates a reflectionwaveform pattern of an event, wherein said executable code thatgenerates a reflection waveform pattern of an event, includes:executable code that simulates said event utilizing an analytical model;and executable code that generates a reflection waveform pattern fromsaid analytical model; executable code that processes said reflectionwaveform pattern to produce a classification reflection waveformpattern; and executable code that stores said classification reflectionwaveform pattern; executable code that adjusts component values of saidanalytical model; executable code that generates a variance arraycorresponding to the adjustment of said component values in saidanalytical model; and executable code that stores said variance array soas to be accessible with said classification reflection waveformpattern.